The 23-year-old has signed a five-year deal, subject to international clearance, for a reported £25 million (27.9 million euros, $32.3 million).
"It's no secret that Jefferson has been someone we have chased for a while this summer," said Bournemouth manager Eddie Howe.
"Jefferson is an extremely talented player and a very good athlete who will bring a different type of play to our midfield.
"He has a lot of qualities that will be suited to the Premier League and I'm really looking forward to working with him."
Lerma, who played all four of Colombia's matches at the World Cup in Russia including the last-16 loss to England, scored three goals in 93 appearances in all competitions over three seasons for Levante.
"I have always loved the Premier League style of football and am very happy to have this opportunity," said Lerma.
"I am looking forward to success and doing important things for this club."
Bournemouth were first promoted to the Premier League in 2015, and finished 12th last season after a ninth-placed effort in the previous campaign.