Ivan Perisic scored a 25th-minute winner to lift the Croatians above Norway after the Scandinavians conceded two second-half goals in a 2-1 defeat at group winners Italy, who also qualified.
The Italians finished on 24 points, four ahead of Croatia and five clear of Norway, with the latter confined to November's two-legged playoffs.
Needing to win and for Norway not to beat Italy, the Croatians laid siege to the home team and missed a string of chances either side of Perisic's goal.
Having squandered two sitters, the winger found the back of the net with a deflected shot from the edge of the penalty area which wrong-footed Malta goalkeeper Andrew Hogg.
After learning that the result in Rome had turned their way, the Croatians endured a nervy last 10 minutes when they sat back on their slender lead.
"It is a fantastic feeling to take Croatia to our ninth major tournament from 11 attempts (as an independent nation)," Croatia coach Ante Cacic told the country's state HRT television.
"All credit to the players for pulling their socks up and grinding out the results we needed after two slip-ups, we deserved to finish in the top two and qualify automatically."
Cacic took over the hot-seat last month from Niko Kovac, who was sacked after a 2-0 defeat in Norway following a 0-0 draw in Azerbaijan.
Croatia's slump in form came after they were deducted a point by UEFA for a bizarre racist incident during their 1-1 home draw with Italy in June.
Croatian fans used a chemical agent to imprint a swastika on the pitch days before the fixture in Split's Poljud stadium and it became visible during the match, which was played behind closed doors because of a previous racism offence.
Cacic, who made his debut in a 3-0 home win over Bulgaria in Zagreb on Saturday, which was also played behind closed doors as part of the punishment for the swastika incident, hoped the Balkan nation's fans would come to their senses.
"Football is Croatia's best product and I am sure our fans will cause no further incidents," he said.
"This outfit has the potential to step out of the 1998 generation's shadows and we are going to France determined to make an impact."
In the 1998 World Cup in France, a talent-packed Croatian team led by their current FA chief Davor Suker finished third after a string of impressive performances, including a 3-0 quarter-final win over Germany.
(Writing by Zoran Milosavljevic in Belgrade; editing by Toby Davis)
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