The 42-year-old is to join the Scot for a trial week in the next month with a view to working with him permanently alongside his main coach Amelie Mauresmo.
The aim will be for Bjorkman to travel with Murray during the weeks when Mauresmo is unavailable, while they will also work together at certain times of the year.
And Murray said he gets on well with the Swede from his playing days.
“We’ve agreed for him to work with us for a week just to try and see how it goes,” he told the BBC.
“I know him very well from when he played. He was one of the older guys when I came on the tour and he was very good to me.
???He’s a very nice person, good sense of humour.
???And he was an exceptional tennis player who made the most of his ability.
“A lot of Swedes turn out to be good coaches. They’ve got a good mindset, they’re very calm individuals and extremely hard workers.”
Bjorkman has not set a date for when he will work with the former Wimbledon champion because he is taking part in Let’s Dance, the Swedish version of Strictly Come Dancing.
Murray, whose mother Judy was a contestant on Strictly Come Dancing, added: “I haven’t seen him dance yet but apparently he’s one of the favourites to win so he must be all right.”
The Briton is in Indian Wells for the first Masters tournament of the season, where he will begin his campaign this weekend against Canadian Vasek Pospisil.