Cook joined Bournemouth from West Yorkshire outfit Leeds 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.
Traditionally, Leeds are a bigger club than Bournemouth and have a bigger fanbase, but things are changing, at least on the pitch.
Former Bournemouth defender Morrell has suggested that Cook’s move from Leeds to the Cherries shows how things are changing.
“Leeds has always been a big club and it has only been in recent years that they have dropped down, mainly due to the finances,” Morrell told The Daily Echo. “They don’t seem to have the resources to get out of the Championship.
"People talk about players going to a small club like Bournemouth but they have to realise things are very different now.
“Our club is punching above its weight with the big boys in the Premier League and they know they have to make these investments in order to stay there.”
“Lewis was clearly a player Leeds thought very highly of and they didn’t want to lose him,” added Morrell. “Everyone expects him to go to the very top and it is encouraging that these players want to come to Bournemouth.”
During the 2015-16 season, Cook scored one goal and created 46 chances in 42 Championship appearances for Leeds.
The 19-year-old midfielder had a pass accuracy of 79% and a shot accuracy of 31%, and won 26 headers, 50 dribbles and 62 tackles.