Lee reached the milestone in 171st ODI when he accounted for the wicket of Darren Sammy during the seven-wicket victory over the West Indies on Sunday.
Waqar took 15 games more than the fiery Aussie paceman.
"I am so honoured and so proud. I don't normally make fuss over these types of things but to reach 300 is a very special feeling and one I will always cherish," Lee said.
"You think about times when you get your baggy green cap or your first Test wicket. And then you think that only two Australians have now achieved this dream of taking 300, it's very special. I am hoping for a few more. The body's feeling great. I am only 31. We'll see what happens," he added.
"I'm very proud to reach 300. When you first start out, you never think you're going to reach 10. And then when you reach 100, you think 200 would be nice. But 300 I never thought in my wildest dreams that I would ever achieve this milestone - In 10, 15 or 20 years' time I will look back and think that this is a very special day for me."
Lee, who has 289 Test wickets, is also on track to scale 300 Test-scalp mark later this year and become the eighth bowler to claim 300 dismissals in both forms of the game.