diff --git a/mysql-test/main/mysql_upgrade.result b/mysql-test/main/mysql_upgrade.result
index 547bd8ae3b7..bde6893526e 100644
--- a/mysql-test/main/mysql_upgrade.result
+++ b/mysql-test/main/mysql_upgrade.result
@@ -920,4 +920,63 @@ GRANT USAGE ON *.* TO `user3`@`%`
 GRANT ALL PRIVILEGES ON `roelt`.`test2` TO `user3`@`%`
 DROP USER 'user3'@'%';
 update mysql.db set Delete_history_priv='Y' where db like 'test%';
+#
+# MDEV-16735 Upgrades only work if 'alter_algorithm' is 'DEFAULT'
+# or 'COPY'. Test that the session value 'DEFAULT' in mysql_upgrade
+# properly overrides the potentially incompatible global value.
+#
+SET GLOBAL alter_algorithm='INPLACE';
+SHOW GLOBAL VARIABLES LIKE 'alter_algorithm';
+Variable_name	Value
+alter_algorithm	INPLACE
+Phase 1/7: Checking and upgrading mysql database
+Processing databases
+mysql
+mysql.column_stats                                 OK
+mysql.columns_priv                                 OK
+mysql.db                                           OK
+mysql.event                                        OK
+mysql.func                                         OK
+mysql.gtid_slave_pos                               OK
+mysql.help_category                                OK
+mysql.help_keyword                                 OK
+mysql.help_relation                                OK
+mysql.help_topic                                   OK
+mysql.host                                         OK
+mysql.index_stats                                  OK
+mysql.innodb_index_stats                           OK
+mysql.innodb_table_stats                           OK
+mysql.plugin                                       OK
+mysql.proc                                         OK
+mysql.procs_priv                                   OK
+mysql.proxies_priv                                 OK
+mysql.roles_mapping                                OK
+mysql.servers                                      OK
+mysql.table_stats                                  OK
+mysql.tables_priv                                  OK
+mysql.time_zone                                    OK
+mysql.time_zone_leap_second                        OK
+mysql.time_zone_name                               OK
+mysql.time_zone_transition                         OK
+mysql.time_zone_transition_type                    OK
+mysql.transaction_registry                         OK
+mysql.user                                         OK
+Phase 2/7: Installing used storage engines... Skipped
+Phase 3/7: Fixing views
+Phase 4/7: Running 'mysql_fix_privilege_tables'
+Phase 5/7: Fixing table and database names
+Phase 6/7: Checking and upgrading tables
+Processing databases
+information_schema
+mtr
+mtr.global_suppressions                            OK
+mtr.test_suppressions                              OK
+performance_schema
+test
+Phase 7/7: Running 'FLUSH PRIVILEGES'
+OK
+SET GLOBAL alter_algorithm=DEFAULT;
+SHOW GLOBAL VARIABLES LIKE 'alter_algorithm';
+Variable_name	Value
+alter_algorithm	DEFAULT
 End of 10.3 tests
diff --git a/mysql-test/main/mysql_upgrade.test b/mysql-test/main/mysql_upgrade.test
index acc4fc31d65..5d8a89b08d4 100644
--- a/mysql-test/main/mysql_upgrade.test
+++ b/mysql-test/main/mysql_upgrade.test
@@ -381,4 +381,17 @@ SHOW GRANTS FOR 'user3'@'%';
 DROP USER 'user3'@'%';
 update mysql.db set Delete_history_priv='Y' where db like 'test%';
 
+--echo #
+--echo # MDEV-16735 Upgrades only work if 'alter_algorithm' is 'DEFAULT'
+--echo # or 'COPY'. Test that the session value 'DEFAULT' in mysql_upgrade
+--echo # properly overrides the potentially incompatible global value.
+--echo #
+
+SET GLOBAL alter_algorithm='INPLACE';
+SHOW GLOBAL VARIABLES LIKE 'alter_algorithm';
+--exec $MYSQL_UPGRADE --force 2>&1
+SET GLOBAL alter_algorithm=DEFAULT;
+SHOW GLOBAL VARIABLES LIKE 'alter_algorithm';
+--remove_file $MYSQLD_DATADIR/mysql_upgrade_info
+
 --echo End of 10.3 tests
diff --git a/scripts/mysql_system_tables_fix.sql b/scripts/mysql_system_tables_fix.sql
index 79866d149bb..47099399722 100644
--- a/scripts/mysql_system_tables_fix.sql
+++ b/scripts/mysql_system_tables_fix.sql
@@ -27,7 +27,7 @@
 set sql_mode='';
 set storage_engine=MyISAM;
 set enforce_storage_engine=NULL;
-set alter_algorithm=DEFAULT;
+set alter_algorithm='DEFAULT';
 
 ALTER TABLE user add File_priv enum('N','Y') COLLATE utf8_general_ci DEFAULT 'N' NOT NULL;