Cook, who already captains England in ODI matches, will begin his career as Test captain against India in November before two Ashes series within a year-and-a-half of each other.
However, the 27-year-old is under no illusions as to the challenge of following Strauss, who is England's second most successful captain ever.
"I'm incredibly proud to be sitting here now as captain of England. It's a huge honour. I'm very excited about the challenge," said Cook.
"I've got huge boots to fill, following Straussy who has done an incredible job. I'm really excited about the challenge ahead, we've got India away and two Ashes series in the next 18 months. There is a lot of cricket to play and hopefully I can do a good job.
"You've got to throw yourself into it, meet the challenge head on and I hope can do that and have got the leadership qualities required."
Strauss won two Ashes series during his spell as captain, as well as guiding England to the top of the Test rankings.