Cook joined Premier League outfit Bournemouth from Championship side Leeds United last week.
As announced on the Cherries’ official website, the 19-year-old midfielder signed a four-year contract with the club.
Bournemouth had to pay Leeds an initial transfer fee of £6 million to secure the services of the talented teenager, according to The Guardian.
It has also been reported by The Guardian that the fee could rise to nearer £10m with add-ons.
Cook has explained his decision to move to Bournemouth, underlining the presence of Howe as the manager as a key factor in the switch from Leeds.
"It's a lovely place to live and the way the club plays really excited me too,” Cook told Bournemouth’s official website.
"The manager has done great things here and likes working with young players. There are quite a few younger players here and I feel that will benefit me and help to progress my career.
"I’m only 19 so I’m still young, you need to look for those managers who want to improve young players and he has the faith in me to try to improve - I’m excited.
"It’s a big change for me, I loved it at Leeds but I felt it was time for a change and I couldn’t say no to playing in the Premier League, it’s every boy's dream. I want to enjoy every moment of it."
Cook is one of the best and most promising young players in England, and has arrived at Bournemouth with a strong reputation.
During the 2015-16 season, Cook scored one goal and created 46 chances in 42 Championship appearances for Leeds.
The young midfielder had a pass accuracy of 79% and a shot accuracy of 31%, and won 26 headers, 50 dribbles and 62 tackles.