The 22-year-old has signed a three-year deal and will join the club in June following the expiry of his Dons deal.
Anderson spent the season on loan at Ayr United and Hamilton Accies, impressing at the latter with his link play and work rate.
Earlier today, Aberdeen confirmed they were signing Livi forward Jay Emmanuel-Thomas.
Anderson exits the Dons after 11 years and 39 games. His most memorable moment came in the Premiership when he netted a last-minute goal against Rangers to earn his side a draw.
"I would like to wish everyone at the club the very best for the future,” he tweeted. “Thank you to the fans for the support you have given me over the years. It was a honour to pull on the red shirt.”
Livi boss David Martindale revealed it was a game on loan at Dunfermline Athletic versus Partick Thistle in 2019 when Anderson was up against experienced defender Steven Anderson which made him sit up and take notice. The forward scored two in a 3-0 win.
He considered signing him last summer.
Martindale told Livingston’s website: “I had spoken to Derek McInnes in the summer with a view to getting Bruce on loan but ironically, I had Jay in on trial and I went with him on that occasion.
“With Bruce, I feel we are getting a young player that has all the attributes to go on and become a top, top player. He’s scored goals in the Premiership already for both Aberdeen and Hamilton and this is what Bruce is all about – scoring goals.
"He is a natural goal scorer and a very good finisher.”
He added: “Bruce will wear the number 9 shirt vacated by JET, who goes in the opposite direction. Brucey has signed a 3-year contract and I’m really looking forward to working with the player closely and seeing what he brings to the group.”
Aberdeen, in a statement confirming his departure, said: “Having been at the Club since he was 11-years-old, we would like to thank Bruce for all his efforts during his time at Pittodrie and wish him all the very best in his future career.”