Goalkeeper Fraser Forster, central defender Virgil van Dijk and midfielder Kris Commons, who are all on the shortlist for Player of the Year, have come from the Scottish champions.
Scottish Cup finalists United are represented by left-back Andrew Robertson, midfielder Stuart Armstrong and striker Nadir Cifti.
League Cup winners Aberdeen have defender Mark Reynolds and midfielder Peter Pawlett in the team while Kilmarnock striker Kris Boyd, the fourth player on the shortlist, and Stevie May, from Scottish Cup finalists St Johnstone, are also included.
Fraser Forster (Celtic), Graeme Shinnie (Inverness), Virgil van Dijk (Celtic), Mark Reynolds (Aberdeen), Andrew Robertson (Dundee Utd), Stuart Armstrong (Dundee Utd), Peter Pawlett (Aberdeen), Kris Commons (Celtic), Stevie May (St Johnstone), Kris Boyd (Kilmarnock), Nadir Cifti (Dundee Utd).
Championship: Michael McGovern (Falkirk), Paul McGinn (Dumbarton), Will Vaulks (Falkirk), Stephen Kingsley (Falkirk), Ziggy Gordon (Hamilton), Anthony Andreu (Hamilton), Mark Millar (Falkirk), Ali Crawford (Hamilton), Kane Hemmings (Cowdenbeath), Rory Loy (Falkirk), Peter McDonald (Dundee).
League One: Cammy Bell (Rangers), Ryan Williamson (Dunfermline), Lee McCulloch (Rangers), Callum Morris (Dunfermline), Lee Wallace (Rangers), Andy Stirling (Stranraer), Andy Geggan (Dunfermline), Nicky Law (Rangers), Michael Moffat (Ayr United), Jon Daly (Rangers), Gavin Swankie (Forfar).
League Two: Graeme Smith (Peterhead), Devon Jacobs (Berwick), Steven Noble (Peterhead), Michael Dunlop (Albion Rovers), Kieran MacDonald (Clyde), Blair Spittal (Queens Park), David Anderson (Queens Park), Lee Currie (Berwick), Kenny MacKay (Annan Athletic), Rory McAllister (Peterhead), Andy Rodgers (Peterhead).