Cook, along with Liverpool striker Dominic Solanke, will join goalkeeper Angus Gunn who was called up on Friday as a replacement for Jack Butland.
The trio played in Friday's Under-21 international against Ukraine in Kiev, and they returned to England to join the senior squad on Saturday evening.
Cook and Solanke were both members of England's U20 squad, which earlier this year were crowned world champions at their age group level.
Striker Solanke has appeared in seven Premier League games this season, while Cook has played in four for the Cherries.
Cook was England's skipper when they lifted the U20 World Cup in Korea, five months ago.
Cook tweeted on Saturday: "Incredibly honoured and proud to be called up for England senior squad. Huge achievement for me and my family."