Confirmation of the trio came at a press conference in Dublin on Wednesday, with Farrell and Howley returning for another Lions trip after working with Gatland during the successful 2013 Australia tour.
Ex-England skipper and current forwards coach Borthwick is a Lions newcomer, but he has made a considerable impression during England’s spectacular unbeaten revival under their Australian head coach Eddie Jones.
Former England assistant coach Farrell was appointed as Ireland defence coach earlier this year, and he helped oversee a first away victory over South Africa, followed by a stunning success against world champions New Zealand in Chicago before a memorable autumn campaign concluded by Ireland defeating Australia.
Attack specialist Howley, who is currently Wales interim head coach while Gatland concentrates on Lions business this season, makes his third successive Lions tour as a coach, while he also toured as a player in 1997 and 2001.
Lions head coach Gatland has not ruled out making a further coaching appointment - the likes of former England and Fiji sevens chief Ben Ryan and Saracens rugby director Mark McCall have both been linked with roles - but he describes the trio as his “core coaching team.”
Gatland said: “I am excited about this coaching team.
“I said from the outset it was important to have continuity because we need to hit the ground running, given the limited preparation time. In Rob and Andy, we have guys who understand the Lions concept, have worked together and know how to coach a winning Lions team.
“It’s also important to have some new input. Steve has done a great job in shaping the England pack and played a major role in their recent run of success, so I am looking forward to working with him.”
The trio will work with their respective countries for the RBS Six Nations Championship in February and March before joining the Lions ahead of the squad announcement on April 19. The Lions management team will be announced in early January.
“We may look to bring in a specialist coach, but fundamentally, this is the core coaching team we believe can help a talented group of players win a Test series in New Zealand,” Gatland added.
Borthwick, who won 57 England caps and made almost 400 appearances for Bath and Saracens, worked with Jones during Japan’s memorable 2015 World Cup campaign that included them defeating South Africa, before joining him again last December after Jones was appointed England boss.
England went unbeaten in 2016, claiming the Six Nations title in Grand Slam fashion, beating Australia three times Down Under and then winning all four autumn Tests.
Borthwick said: “There have been some fantastic Lions forwards coaches in the past - Jim Telfer, Andy Robinson, Warren himself, Graham Rowntree - and it’s a real privilege to be chosen. It’s a brilliant challenge.
“We’ve seen some fantastic results from the home nations in the recent autumn series and some brilliant performances by the players. That all bodes well for the Lions.”
Farrell added: “The Lions is a unique experience for players and coaches. To bring together the best players from four countries and go to the home of the world champions to take them on in their own back-yard - that’s pretty special.
“As a group, we are going to be tested across the board against the number one-ranked team in the world.
“The challenge for us will be to get on the same page as quickly as possible, appreciate fully the danger they pose and find solutions to their attacking threats.”
And Howley said: “The British and Irish Lions is at the pinnacle of international rugby. We have a responsibility to uphold its tradition and heritage, and build on the success of the 2013 tour.
“This will be my fifth tour with the Lions, but my first to New Zealand. We are under no illusions what to expect on the field, but with the inspirational travelling support from all four home nations behind us, I believe it will be a memorable six weeks.
“As a coach, the experiences in 2009 and 2013 were hugely-rewarding, and I would like to thank the WRU (Welsh Rugby Union) for once again supporting the role and understanding the benefits we can take forward from this opportunity.”