Lawson, 49, was picked by a four-member Pakistan Cricket Board (PCB) committee over two other Australians, Dav Whatmore and Richard Done. The trio were all interviewed last month.
"Of the three, Lawson has been confirmed. We had three outstanding coaches," PCB Chairman Nasim Ashraf told a press conference.
Lawson was awarded a two-year contract open for renewal "as we want a coach to lead us to the 2011 World Cup," which will jointly be hosted by Pakistan, Ashraf said.
Lawson took 180 wickets in 46 Tests and 88 in 79 one-day internationals for Australia between 1980-89.
He said earlier that he regarded the position - seen as one of the most difficult in the game -- as "a wonderful challenge."
"It's such a talented squad they have over there," he told Sky News.
"When you look at the class of player they have, you just have to be excited about being involved with them."
Lawson has no direct experience as an international coach. But he has coached the New South Wales team in Australia and was reportedly backed by most of the Pakistan team's players, who found him more friendly.
Reports in Australia said it was believed the Pakistan board had wanted Whatmore, who has coached Sri Lanka and Bangladesh, but went with the players' wishes.
Pakistan have had 11 different coaches in the past 10 years, with three stints each for former great Javed Miandad and Richard Pybus, Pakistan's first foreign coach.
Woolmer, who took over from Miandad in June 2004, was criticised for over-experimenting with the team and was certain to be sacked after Pakistan's first-round exit from the 2007 World Cup.
The new coach will be under pressure from the outset as Pakistan have a hectic international schedule commencing with the Twenty20 World Cup in September in South Africa.
Pakistan then host South Africa for two Tests and five one-day internationals before touring India for three Tests and five one-day internationals in November and December.
Pakistan also face world champions Australia in March and April next year.
Lawson said he expected to head over to Lahore within a month to prepare for the Twenty-20 World Cup.
"What changes when we get there? Well, there'll probably be quite a few. I'm hoping to take a few more Australian personnel with me as well," he said.
The announcement ends a worldwide search for a new Pakistan coach that began when Woolmer was found dead in his hotel room in Jamaica on March 18, the day after Pakistan lost to minnows Ireland in the first round of the World Cup.
Woolmer's death was at first treated as a murder - with a flurry of speculation linking the death to a so-called "match-fixing mafia" - before the Jamaican police last month admitted he had died of natural causes.
Lawson's appointment meanwhile is a double blow for Whatmore, who was also snubbed by Pakistan's bitter rivals India after being the frontrunner in their campaign to find a new coach.
Whatmore guided Sri Lanka to a World Cup title in 1996 and also took Bangladesh to an unexpected second round in the World Cup 2007.