Cook has been selected in a bowling attack that includes fellow pacemen Josh Tongue and Gus Atkinson as well as spinner Shoaib Bashir while captain Ben Stokes is also expected to play a part with the ball after undergoing hamstring surgery in January.
The 27-year-old Cook has taken 321 wickets in 89 first-class matches at an average of less than 20 and benefits from the injury-enforced absence of Chris Woakes and the retirement of James Anderson.
"I'm obviously very excited about getting the nod and getting out there," Cook told reporters at Trent Bridge. "It's any young cricketer's dream to pull on the Test shirt for England.
"So it's something hopefully that comes to fruition and I'm really, really looking forward to it.
"I feel, at 27, a better cricketer for the experiences I've had in the game," he said. "I think the Lions programme and being in and around the Test set-up over the last few years has made that transition into the squad pretty seamless, and I felt very welcomed.
"The environment's been fantastic to be a part of. I'm just excited at the prospect of what's to come and trying to get stuck in and take some wickets."
England Test XI: 1 Zak Crawley, 2 Ben Duckett, 3 Ollie Pope, 4 Joe Root, 5 Harry Brook, 6 Ben Stokes (capt), 7 James Smith (wk), 8 Gus Atkinson, 9 Josh Tongue, 10, Sam Cook, 11 Shoaib Bashir
Brian Bennett scored Zimbabwe's fastest ever Test century but England were still well on top after two days of the historic one-off fixture at Trent Bridge in Nottingham.
Jofra Archer has been ruled out England's ODI series against West Indies, that starts later this month, due to a thumb injury sustained with IPL side Rajasthan Royals.
Captain Ben Stokes is "very confident" he can fulfill his role as an all-rounder in England's Test team ahead of a busy home schedule as he returns from hamstring surgery.
England have confirmed that New Zealand legend Tim Southee has joined the coaching staff as a 'specialist skills consultant'.
