The transfer fee for Lerma was not disclosed, but British media reported that he was moving for 25 million pounds ($32 million), which beats the previous record of 20 million pounds the club paid for Dutch defender Nathan Ake from Chelsea last year.
"The transfer has been very long because it took a while for the clubs to reach an agreement, but the most important thing is that I am here now and everyone got what they wanted in the end," Lerma told the club website http://www.afcb.co.uk/news/first-team/lerma-signs-in-club-record-deal.
"I have always loved the Premier League style of football and am very happy to have this opportunity. I am looking forward to success and doing important things for this club."
Lerma started out with Colombian side Atletico Huila and joined Spanish Liga club Levante in 2015, initially on loan, playing 93 games in all competitions and scoring three goals.
He made his Colombia debut in November 2017, featuring nine times so far, and played at the 2016 Olympics.
"Jefferson is an extremely talented player and a very good athlete who will bring a different type of play to our midfield," said Cherries manager Eddie Howe.
He is the club's third close-season signing after Sheffield United midfielder David Brooks and Leganes full-back Diego Rico.
Bournemouth chief executive Neill Blake added: "It hasn’t been easy and we have had to be patient, but we have got our man and it is a huge statement for this club.
"A new record transfer speaks volumes of the ambition of our owners to continue progressing the club and competing in the Premier League."
($1 = 0.7731 pounds)
(Writing by Ken Ferris; Editing by Hugh Lawson)
