Strauss is joined by another South African-born player in Edinburgh prop Willem Nel, who has won two caps after qualifying through residency this year, and New Zealand-born John Hardie, who is currently without a club and made his Scotland debut last month.
Among the notable absentees were other "Kilted Kiwis" Hugh Blake and Blair Cowan and fellow flanker John Barclay.
Cowan started all five of Scotland's games in this year's Six Nations while Barclay had been widely expected to be included having been recalled for the warmup clashes with Ireland and Italy after an absence of nearly two years.
Scrumhalf Greig Laidlaw captains a squad of 17 forwards and 14 backs that has a total of 651 caps with three members -- Alasdair Dickinson, Ross Ford and Sean Lamont -- due to play in their third World Cup.
"It's been a tough but rewarding two months," said Cotter. "We're proud of the effort everyone has put in to this point.
"Getting down to 31 has been a difficult process because all the players have represented themselves well in the opportunities given.
"There are some good players and good people who haven't made it. We obviously feel for them and would like to thank them for all their efforts."
Having lost to Ireland and beaten Italy twice, Scotland face France in Paris on Saturday in their final warm-up match before heading to the tournament in England, where they will play South Africa, Samoa, Japan and the United States in Pool B.
Scotland squad:
Forwards: Alasdair Dickinson, Ryan Grant, Gordon Reid, Willem Nel, Jon Welsh, Fraser Brown, Ross Ford, Stuart McInally, Grant Gilchrist, Jonny Gray, Richie Gray, Tim Swinson, David Denton, John Hardie, Josh Strauss, Alasdair Strokosch, Ryan Wilson.
Backs: Sam Hidalgo-Clyne, Greig Laidlaw (captain), Henry Pyrgos, Finn Russell, Duncan Weir, Mark Bennett, Peter Horne, Matt Scott, Richie Vernon, Sean Lamont, Sean Maitland, Tommy Seymour, Tim Visser, Stuart Hogg.
(Reporting by Mitch Phillips, editing by Clare Fallon and Neville Dalton)
