The 23-year-old, who starred for Colombia at the 2018 World Cup, had been linked with the Cherries for a number of weeks.
Bournemouth announced the news on Tuesday night, confirming that Lerma had joined the Premier League outfit for a club transfer record sum but not disclosing the amount.
According to Sky Sports News, the two clubs had agreed a £25m fee which eclipses the club's record outlay, set last summer when they signed Nathan Ake for £20m from Chelsea.
"I'm so happy to be an AFC Bournemouth player," Lerma told the official club site.
"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.
"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."
Eddie Howe's side kick off their Premier League campaign at home on August 11 to Cardiff City.