For 27-year-old Daley, the feat marks his first Olympic gold at his fourth Games, while Lee, 23, succeeds on his Olympic debut.
The pair dethroned champions China by a margin of just over a point thanks to a stunning final dive - the forward 4-1/2 somersaults - which earned 101.52 points.
Daley and Lee become just GB's second diving Olympic gold medallists in history, following on from Chris Mears and Jack Laugher's triumph in the 3m synchro at Rio 2016, and put Team GB firmly on course for its best ever diving haul.
Daley now has another shot at gold when he takes on the individual 10m platform event along with teammate Noah Williams on Friday and Saturday.
Final leaderboard in full:
1. Tom Daley, Matty Lee (GBR) - 471.81
2. Cao Yuan, Chen Aisen (CHN) - 470.58
3. Aleksandr Bondar, Viktor Minibaev (ROC) - 439.92
4. Diego Balleza, Kevin Berlin (MEX) - 407.31
5. Vincent Riendeau, Nathan Zsombor-Murray (CAN) - 405.00
6. Oleh Serbin, Oleksil Sereda (UKR) - 400.44
7. Kim Yeongnam, Woo Haram (KOR) - 396.12
8. Hiroki Ito, Kazuki Murakami (JPN) - 377.10