Fellow centre Duncan Taylor, of Saracens, is back after missing the autumn Tests through injury.
Uncapped Edinburgh forwards Simon Berghan and Cornell du Preez are included but David Denton is not fit.
Alasdair Dickinson is also absent through injury, while fellow Edinburgh prop WP Nel is listed but is a doubt with a neck problem.
Nel lasted just 27 minutes of his return from a long injury lay-off at the weekend and is awaiting the results of a scan.
This year's championship will be New Zealander Cotter's last in charge of the national side.
He will take over as Montpellier coach this summer and will be replaced by Glasgow Warriors' Gregor Townsend.
The Scots open their Six Nations campaign at home to Ireland on 4 February before facing France away eight days later.
With Dickinson missing and doubts over Nel, Newcastle front-rower Jon Welsh returns for the first time since the 2015 World Cup.
John Hardie, who started all five matches in last year's tournament, is another Edinburgh player in Cotter's plans working his way back to fitness.
Edinburgh lock Ben Toolis is also selected having not appeared since the Six Nations of 2015.
"It's a well-balanced and exciting group that have played a lot of rugby together, know each other well and are ambitious to do well in a Scotland jersey," said Cotter.
"I think if we get our mind-set right we can be competitive and push for wins in every game in this campaign."
Last year, Scotland finished fourth in the championship after victories against Italy and France.
In November's autumn Tests, the Scots beat Argentina and Georgia after a narrow defeat by Australia.
BBC Scotland's Tom English
The competition in Scotland's midfield is now fierce. This is probably - almost certainly - the best set of centres the country has ever had. Cotter has named five - Mark Bennett, Alex Dunbar, Huw Jones, Matt Scott and Duncan Taylor.
Alasdair Dickinson's injury is a blow. Scotland could do with his experience at loosehead.
Scotland squad:
Forwards: Alex Allan, Zander Fagerson, Gordon Reid (all Glasgow Warriors), Simon Berghan, Allan Dell, Willem Nel (all Edinburgh Rugby), Jon Welsh (Newcastle Falcons), Fraser Brown (Glasgow Warriors), Ross Ford, Stuart McInally (both Edinburgh Rugby), Jonny Gray (Glasgow Warriors), Richie Gray (Toulouse), Grant Gilchrist (Edinburgh Rugby), Tim Swinson (Glasgow Warriors), Ben Toolis (Edinburgh Rugby), John Barclay (Scarlets), Cornell Du Preez, John Hardie, Hamish Watson (all Edinburgh Rugby), Rob Harley, Josh Strauss, Ryan Wilson (all Glasgow Warriors)
Backs: Greig Laidlaw (Gloucester), Ali Price, Henry Pyrgos, Finn Russell (all Glasgow Warriors), Duncan Weir (Edinburgh Rugby), Mark Bennett, Alex Dunbar (Glasgow Warriors), Huw Jones (Stormers), Matt Scott (Gloucester), Duncan Taylor (Saracens), Stuart Hogg (Glasgow Warriors), Damien Hoyland (Edinburgh Rugby), Sean Maitland (Saracens), Tommy Seymour (Glasgow Warriors), Tim Visser (Harlequins)
4 February - Scotland v Ireland (14:25)
12 February - France v Scotland (15:00)
25 February - Scotland v Wales (14:25)
11 March - England v Scotland (16:00)
18 March - Scotland v Italy (12:30)
Scotland head coach Vern Cotter has recalled Gloucester centre Matt Scott to his squad ahead of the Six Nations.