Bjorn captained Europe to victory at Le Golf National in Paris in 2018, played in the biennial contest three times and was a vice-captain on four previous occasions.
Stenson, who was one of Bjorn's 12 players in Paris, said: "I have known Thomas for my whole career.
"I trust him implicitly and I know any advice he will give me will be honest and direct.
"He will not simply tell me what he thinks I want to hear and that will be important, so I'm delighted to have him as my first vice-captain for Rome.
"Since the match itself is still over a year away, I know I am going to have a lot of conversations with him about all elements of the Ryder Cup from his experience, both as a vice-captain on previous occasions but also, obviously, as the captain in 2018 when we had a great result.
"I will be depending on him a lot and I'm really looking forward to those chats.
"He was very happy when I asked him. He was very honoured to be asked and happy to be part of Team Europe again and part of the journey with the players."
Bjorn added: "I'm delighted to be part of the whole Ryder Cup experience once again.
"I probably thought that after 2018 that was it for me, but Henrik called me to talk about captaincy in general and that led into him asking me if I wanted to do another stint as vice-captain, which I agreed to. I'm excited to work with him.
"I think I can help Henrik outline what he wants to do with his captaincy going forwards. I can keep asking him the right questions and reminding him of things that are going to come his way that he might not have thought about.
"I will help him prepare in the best possible way and, as we get closer to the match, to be an additional support to the players.
"I think Henrik will be a fantastic captain. He is so well respected by players and by everyone in the game. He is a very hard-working golfer and somebody who is true to himself, and his team will represent that.
"He has a great sense of humour that the players will take to, and he is very well liked across the whole Tour, not just the top where he has played his golf for so many years."
Europe will seek to regain the trophy at Marco Simone Golf and Country Club from September 29-October 1 following the record 19-9 defeat to the United States at Whistling Straits last year.