Cook's place in the England team at Trent Bridge on Thursday is a reward for a sustained spell as one of county cricket's most consistent wicket-takers with Essex.
The 27-year-old's 227 County Championship wickets are the most by any seamer over the last five years.
Cook's 321 first-class wickets have come at an average of only 19.85.
Tongue, who missed the whole of last season with a pectoral injury, has also been picked in England's new-look bowling attack in his first appearance since the 2023 Ashes series.
The clash with Zimbabwe is only England's second home Test without retired fast bowlers James Anderson and Stuart Broad, and the injured Chris Woakes, in the past 18 years.
"I've been incredibly fortunate to have been a fan growing up watching those guys. They are some of the best who have ever done it and people I've tried to emulate," Cook said of following in Anderson and Broad's footsteps.
"They're tough acts to follow, aren't they? But as a fan and as a bowler, trying to sort of learn from them and watch them, it's been very valuable.
"I think it's probably driven me on and made me a better bowler for it. I certainly trust what I do and feel comfortable in my own skin."
Gus Atkinson joins Cook and Tongue as the main pace bowlers, leaving no place for Durham's Matthew Potts, with uncapped batsman James Rew also missing out.
Cook will hope to add several Zimbabwe players to the 'little black book' he keeps to record the names of opponents he gets out.
"It started as a bit of a joke when I was younger. It's something I can look back on when I finish playing. It'll be a nice memento," he said.
"There'll be some good names in there and a few more to come hopefully.
"When I was quite young I got Joe Root's first ball. I'll let him know about that one. Maybe he can sign it this week."
Shoaib Bashir retains his spot as England's spinner despite taking just two wickets in his loan spell at Glamorgan.
England captain Ben Stokes is expected to bowl occasionally after the all-rounder's lengthy rehabilitation from his latest hamstring tear.
Zak Crawley has been retained as one of England's opening batsmen alongside Ben Duckett.
Ollie Pope moves to number three in the batting order, with Joe Root at four and Harry Brook at five.
Jamie Smith is back as wicketkeeper after paternity leave.
The four-day Zimbabwe Test is a warm-up for England's five-match series against India before they head to Australia for the Ashes later this year.