The England captain scored twice as Gareth Southgate's men came from behind at Wembley.
Gianluca Scamacca put the European champions ahead early but Kane scored from the penalty spot to level.
Marcus Rashford put England ahead after the break and Kane scored again to seal the three points.
England top Group C on 16 points from six games and cannot now be caught, leaving Italy and Ukraine to scrap it out for second place.
"It's never as easy as it looks," Kane told Channel 4. "We have had a really tough group this time but credit to the lads, some of the results we've had, performances and we topped it off here today.
"We went 1-0 down, we stayed calm and we stayed steady, we knew we had enough to get the win and we did it.
"It has been a tough journey and to qualify with two games to go is credit to everyone involved."
FT: 🏴 3-1 🇮🇹— SuperSport Football ⚽️ (@SSFootball) October 17, 2023
Harry Kane makes history as England secure qualification for #EURO2024 ✅
You can watch the end of France against Scotland on SS Football 📺
📺 Stream it here: https://t.co/TesYUfo62x pic.twitter.com/FVnCdDymVW
Kane is now England's top scorer at Wembley, overtaking Bobby Charlton.
"I love it, it's our home, we've made it a real fortress over the years and with a full house here, the fans are loving it, we wanted to repay them with good victories and good performances and we did that today," he said.