It means both the County's red and white ball skippers will miss out on playing the the Steelbacks' Royal London One Day Cup campaign in August.
Wicket-keeper/batsman and red ball captain Rossington enjoyed a strong season for the Lord's-based Spirit in 2021, even though the team endured a terrible opening campaign.
Captained by England World Cup winner Eoin Morgan, Spirit finished rock-bottom of the table after winning just one of their eight group games, and will be desperate to do better in 2022.
In an attempt to do just that, the axe has been wielded by Spirit head coach Shane Warne, with only 10 players being retained from their 16-man squad.
Rossington is one of those, with the 28-year-old being rewarded for some solid innings with the bat in hand at the top of the order, and his reliable glove work.
In his six innings, Rossington scored 140 runs at 23.33 with a strike-rate of more than 152 and a top score of 46. He also claimed four catches behind the stumps, and made two stumpings.
Cobb also gets a second chance with the Welsh Fire, despite a disappointing campaign last time out.
The Steelbacks skipper played only four of Fire's group matches, scoring just 42 runs with a top score of 28 not out, while he also only bowled three overs of off-spin.
But he has been retained by the Cardiff-based Franchise, that also includes his former Northants team-mate Ben Duckett.
Graeme White has not been retained by Fire after he was a late call-up last year, while Brandon Glover has been dropped by the Oval Invincibles.
The South African-born pace bowler failed to bowl a ball in anger for the Oval-based franchise in the 2021 competition as he was sidelined throughout.
The Steelbacks' Vitality T20 Blast overseas signing for the summer, New Zealand's Jimmy Neesham, has not been retained by Fire who he played for last summer.
Mohammad Nabi, who played for Steelbacks in the Blast last summer before teaming up with London Spirit, has been released by the Lord's-based team.
Aside from Rossington and Cobb, no other Northants players have been picked by any of the eight franchises in the initial selections.
They will be hoping to be picked up in the Draft, which will take place on Wednesday, March 30, while there will also be a wildcard slot left open at each of the eight teams.
These will be filled following the T20 Blast competition, meaning players have the chance to catch the eye in that competition.
Elsewhere, former Northants all-rounder David Willey has been retained by Northern Superchargers.
Hundred squad retained lists
BIRMINGHAM PHOENIX: Chris Woakes, Liam Livingstone, Moeen Ali (captain), Adam Milne (Overseas), Benny Howell, Tom Abell, Will Smeed, Chris Benjamin, Miles Hammond, Henry Brookes
LONDON SPIRIT: Zak Crawley, Mark Wood, Glenn Maxwell (Overseas), Eoin Morgan (captain), Mason Crane, Dan Lawrence, Adam Rossington, Ravi Bopara, Blake Cullen, Brad Wheal
MANCHESTER ORIGINALS: Jos Buttler, Ollie Robinson, Phil Salt, Matt Parkinson, Jamie Overton, Tom Hartley, Tom Lammonby, Colin Ackermann, Wayne Madsen, Fred Klaassen, Calvin Harrison
NORTHERN SUPERCHARGERS: Ben Stokes, Adil Rashid, David Willey, Faf du Plessis (Overseas), Harry Brook, Brydon Carse, Matty Potts, John Simpson, Adam Lyth, Callum Parkinson
OVAL INVINCIBLES: Sam Curran, Rory Burns, Jason Roy, Sam Billings (captain). Tom Curran, Will Jacks, Saqib Mahmood, Reece Topley, Jordan Cox, Nathan Sowter
SOUTHERN BRAVE: Jofra Archer, Marcus Stoinis (Overseas), James Vince (captain), Tymal Mills, Chris Jordan, George Garton, Alex Davies, Jake Lintott, Tim David (Overseas), Ross Whiteley, Craig Overton
TRENT ROCKETS: Joe Root, Dawid Malan, Rashid Khan, Alex Hales, Lewis Gregory (captain), Marchant De Lange (Overseas), Luke Wood, Samit Patel, Matt Carter, Steven Mullaney, Sam Cook, Tom Moores
WELSH FIRE: Jonny Bairstow, Ollie Pope, Ben Duckett, Jake Ball, David Payne, Leus du Plooy, Matt Critchley, Ryan Higgins, Josh Cobb