Strachan said: "I've named a big squad for this match because I feel that it's important to get as many of the players together as possible ahead of my first match as national coach.
"I want to have a strong squad for the match against Estonia, which will help us to prepare for the World Cup qualifying double-header against Wales and Serbia in March.
"I'm looking forward to getting started in earnest, and can't wait to lead the team out at Pittodrie next week."
Goalkeepers
Matt Gilks (Blackpool)
David Marshall (Cardiff City)
Allan McGregor (Besiktas)
Defenders
Phil Bardsley (Sunderland)
Christophe Berra (Wolverhampton Wanderers)
Gary Caldwell (Wigan Athletic)
Grant Hanley (Blackburn Rovers)
Alan Hutton (Real Mallorca)
Russell Martin (Norwich City)
Charlie Mulgrew (Celtic)
Lee Wallace (Rangers)
Andy Webster (Heart of Midlothian)
Midfielders
Charlie Adam (Stoke City)
Scott Brown (Celtic)
Chris Burke (Birmingham City)
Kris Commons (Celtic)
James Forrest (Celtic)
James McArthur (Wigan Athletic)
James Morrison (West Bromwich Albion)
Matt Phillips (Blackpool)
Robert Snodgrass (Norwich City)
Forwards
Steven Fletcher (Sunderland)
Ross McCormack (Leeds United)
Jamie Mackie (Queens Park Rangers)
Shaun Maloney (Wigan Athletic)
Kenny Miller (Vancouver Whitecaps)
Steven Naismith (Everton)
Jordan Rhodes (Blackburn Rovers)