diff --git a/lib/classes/date.php b/lib/classes/date.php
index 3685809eb4f..a2b4a6b9361 100644
--- a/lib/classes/date.php
+++ b/lib/classes/date.php
@@ -72,8 +72,12 @@ class core_date {
 
         if (is_numeric($currentvalue)) {
             // UTC offset.
-            $modifier = ($currentvalue > 0) ? '+' : '';
-            $a = 'UTC' . $modifier . number_format($currentvalue, 1);
+            if ($currentvalue == 0) {
+                $a = 'UTC';
+            } else {
+                $modifier = ($currentvalue > 0) ? '+' : '';
+                $a = 'UTC' . $modifier . number_format($currentvalue, 1);
+            }
             $timezones[$currentvalue] = get_string('timezoneinvalid', 'core_admin', $a);
         } else {
             // Some string we don't recognise.
@@ -508,7 +512,7 @@ class core_date {
         );
 
         // Legacy GMT fallback.
-        for ($i = -14; $i <= 13; $i++) {
+        for ($i = -12; $i <= 14; $i++) {
             $off = abs($i);
             if ($i < 0) {
                 $mapto = 'Etc/GMT+' . $off;
diff --git a/lib/tests/date_test.php b/lib/tests/date_test.php
index 3e4d908787e..2cd0d9f7329 100644
--- a/lib/tests/date_test.php
+++ b/lib/tests/date_test.php
@@ -77,7 +77,7 @@ class core_date_testcase extends advanced_testcase {
         $this->assertSame('Pacific/Auckland', core_date::normalise_timezone(-14));
         $this->assertSame('Etc/GMT-12', core_date::normalise_timezone(12));
         $this->assertSame('Etc/GMT-13', core_date::normalise_timezone(13));
-        $this->assertSame('Pacific/Auckland', core_date::normalise_timezone(14));
+        $this->assertSame('Etc/GMT-14', core_date::normalise_timezone(14));
 
         $this->assertSame('Asia/Kabul', core_date::normalise_timezone(4.5));
         $this->assertSame('Asia/Kolkata', core_date::normalise_timezone(5.5));
@@ -107,7 +107,7 @@ class core_date_testcase extends advanced_testcase {
         $this->assertSame('Pacific/Auckland', core_date::normalise_timezone(-14));
         $this->assertSame('Etc/GMT-12', core_date::normalise_timezone(12));
         $this->assertSame('Etc/GMT-13', core_date::normalise_timezone(13));
-        $this->assertSame('Pacific/Auckland', core_date::normalise_timezone(14));
+        $this->assertSame('Etc/GMT-14', core_date::normalise_timezone(14));
 
         $this->setTimezone('Pacific/Auckland', 'Pacific/Auckland');
         $tz = new DateTimeZone('Pacific/Auckland');
@@ -334,6 +334,76 @@ class core_date_testcase extends advanced_testcase {
         $this->assertSame('Etc/GMT-1', date_default_timezone_get());
     }
 
+    public function legacyUserTimezoneProvider() {
+        return [
+            ['', 'Australia/Perth'],            // Fallback on default timezone.
+            ['-13.0', 'Australia/Perth'],       // Fallback on default timezone.
+            ['-12.5', 'Etc/GMT+12'],
+            ['-12.0', 'Etc/GMT+12'],
+            ['-11.5', 'Etc/GMT+11'],
+            ['-11.0', 'Etc/GMT+11'],
+            ['-10.5', 'Etc/GMT+10'],
+            ['-10.0', 'Etc/GMT+10'],
+            ['-9.5', 'Etc/GMT+9'],
+            ['-9.0', 'Etc/GMT+9'],
+            ['-8.5', 'Etc/GMT+8'],
+            ['-8.0', 'Etc/GMT+8'],
+            ['-7.5', 'Etc/GMT+7'],
+            ['-7.0', 'Etc/GMT+7'],
+            ['-6.5', 'Etc/GMT+6'],
+            ['-6.0', 'Etc/GMT+6'],
+            ['-5.5', 'Etc/GMT+5'],
+            ['-5.0', 'Etc/GMT+5'],
+            ['-4.5', 'Etc/GMT+4'],
+            ['-4.0', 'Etc/GMT+4'],
+            ['-3.5', 'Etc/GMT+3'],
+            ['-3.0', 'Etc/GMT+3'],
+            ['-2.5', 'Etc/GMT+2'],
+            ['-2.0', 'Etc/GMT+2'],
+            ['-1.5', 'Etc/GMT+1'],
+            ['-1.0', 'Etc/GMT+1'],
+            ['-0.5', 'Etc/GMT'],
+            ['0', 'Etc/GMT'],
+            ['0.0', 'Etc/GMT'],
+            ['0.5', 'Etc/GMT'],
+            ['1.0', 'Etc/GMT-1'],
+            ['1.5', 'Etc/GMT-1'],
+            ['2.0', 'Etc/GMT-2'],
+            ['2.5', 'Etc/GMT-2'],
+            ['3.0', 'Etc/GMT-3'],
+            ['3.5', 'Etc/GMT-3'],
+            ['4.0', 'Etc/GMT-4'],
+            ['4.5', 'Asia/Kabul'],
+            ['5.0', 'Etc/GMT-5'],
+            ['5.5', 'Asia/Kolkata'],
+            ['6.0', 'Etc/GMT-6'],
+            ['6.5', 'Asia/Rangoon'],
+            ['7.0', 'Etc/GMT-7'],
+            ['7.5', 'Etc/GMT-7'],
+            ['8.0', 'Etc/GMT-8'],
+            ['8.5', 'Etc/GMT-8'],
+            ['9.0', 'Etc/GMT-9'],
+            ['9.5', 'Australia/Darwin'],
+            ['10.0', 'Etc/GMT-10'],
+            ['10.5', 'Etc/GMT-10'],
+            ['11.0', 'Etc/GMT-11'],
+            ['11.5', 'Etc/GMT-11'],
+            ['12.0', 'Etc/GMT-12'],
+            ['12.5', 'Etc/GMT-12'],
+            ['13.0', 'Etc/GMT-13'],
+        ];
+    }
+
+    /**
+     * @dataProvider legacyUserTimezoneProvider
+     * @param string $tz The legacy timezone.
+     * @param string $expected The expected converted timezone.
+     */
+    public function test_get_legacy_user_timezone($tz, $expected) {
+        $this->setTimezone('Australia/Perth', 'Australia/Perth');
+        $this->assertEquals($expected, core_date::get_user_timezone($tz));
+    }
+
     public function test_get_user_timezone() {
         global $CFG, $USER;
         $this->resetAfterTest();
diff --git a/lib/tests/moodlelib_test.php b/lib/tests/moodlelib_test.php
index 229e918186b..f74df9382db 100644
--- a/lib/tests/moodlelib_test.php
+++ b/lib/tests/moodlelib_test.php
@@ -1582,7 +1582,7 @@ class core_moodlelib_testcase extends advanced_testcase {
                 'expectedoutput' => '1309485600'
             ),
             array(
-                'usertimezone' => '14', // Server time.
+                'usertimezone' => '-14', // Server time.
                 'year' => '2011',
                 'month' => '7',
                 'day' => '1',