Lawson said he received a call from the Pakistan Cricket Board on Sunday confirming his appointment as successor to Woolmer, whose mysterious death at the cricket World Cup in March sparked a murder investigation in the Caribbean.
The PCB was expected to make an official announcement later today.
Lawson, 49, took 180 wickets in 46 Tests for Australia between 1980-1989. He has never coached before at international level, but beat fellow Australians Dav Whatmore and Richard Done to the post.
“It's a challenge, I think it's a wonderful challenge to have because it's such a talented squad they have over there.
“They're coming off a poor World Cup and controversially being beaten by Ireland, and all the things that accompany that, but when you look at the class of player they have you've just got to be excited about being involved with them.''
Lawson's appointment follows the recent recruitment of Trevor Bayliss to succeed fellow Australian Tom Moody as coach of Sri Lanka.
Lawson says he expects to arrive at Pakistan in the next month.
Pakistan doesn’t play again until the Twenty20 World Cup at South Africa in September.
“Probably in the next month I'll be heading over to Lahore to their academy to prepare for the Twenty20 World Cup,”
“Then Pakistan have a huge series against India which is their sort of Ashes-style series.''
Lawson, a trained optometrist, has helped with the New South Wales state cricket team and has worked as a cricket commentator since retiring from playing.