Alam will take the helm for Pakistan's upcoming series of three one-day internationals against the West Indies in November in the neutral venue of Abu Dhabi.
"We have appointed Intikhab as the coach as we found him to be the suitable candidate," PCB chairman Ijaz Butt told AFP. "He will accompany the team to Abu Dhabi for the one-day internationals against the West Indies."
The PCB sacked former Australian Test fast bowler Lawson on Friday after a string of poor results. He had spent just 15 months in the job, regarded as one of the toughest in world cricket.
The 66-year-old Alam has also been Pakistan coach and manager on several occasions, most notably during Pakistan's World Cup title win in 1992. Former captain and master batsman Javed Miandad was also a candidate for the post.
Butt said the length of Alam's contract was expected to be decided next week.
"We would like to appoint Alam for a two-year contract, but we have to get final approval from the members of the governing board," said Butt, who took over as chairman earlier this month.
Pakistan sacks coach Lawson
Alam said he would try to do his best for Pakistan.
"It's a big responsibility," Alam told AFP.
"It is not an easy job and I have taken up this assignment as a big challenge," said Alam, who will abandon his contract with Punjab in India, where he was to take over this month.
Alam said discipline would be his top priority for the controversy-hit Pakistan side.
"I will try to maintain discipline because no player is bigger than the game and discipline has been our problem, so that will be my top priority," said Alam, who played 47 Tests between 1959-75 and also led Pakistan in 17 Tests.
As a quality leg-spinner he took 125 wickets, his first coming on his first delivery in Test cricket against Australia in 1959.