Both Howley and Rowntree will be undertaking their second Lions tours and Farrell will be on his first.
"I am delighted with today's appointments and confident that Rob, Graham, Andy and myself can come together quickly to face one of the hardest rugby challenges," Gatland told a news conference in Edinburgh on Wednesday.
"Lions tours are unique as we have to mould together players from four different countries in an incredibly short space of time."
The Lions begin the tour with a match against the Barbarians on June 1 in Hong Kong before travelling to Australia where they play five warm-up matches ahead of the first of three games against the Wallabies. (Reporting By Mark Pangallo, editing by Ed Osmond)