Northern Irishman Clarke made the announcement at the BMW PGA Championship at Wentworth and he is planning to appoint two more deputies later in the season.
Irishman Harrington, 44, who has featured in six Ryder Cups as a player, was also a vice-captain under Paul McGinley when Europe won by 16 1/2 points to 11 1/2 at Gleneagles, Scotland two years ago.
It will be the fourth time Bjorn has served as an assistant captain. The 45-year-old Dane played in the biennial team event in 1997, 2002 and 2014.
Lawrie will act as a deputy for the first time. The 47-year-old Scot was a member of the losing European team in 1999 and the winning side in 2012.
U.S. skipper Davis Love III is also planning to use five deputies at Hazeltine, Minnesota.
Love has already announced that Tiger Woods, Tom Lehman, Steve Stricker and Jim Furyk will be in his backroom team.
The 2016 Ryder Cup runs from September 30 to October 2.
(Editing by Ed Osmond)
