The Glasgow captain and back-rower qualifies for Scotland on residential grounds on 19 September, a day after the tournament begins and four days before his adopted nation’s first match, against Japan at Kingsholm on 23 September.
Strauss is joined by another South African-born player in Edinburgh prop WP Nel, who has won two caps since qualifying for Scotland in June.
Meanwhile, Richie Vernon’s transformation from back-row to centre takes on another level after he was named in the squad.
Vernon made the positional switch 18 months ago and becomes the first player to be selected for Scotland in a Rugby World Cup as both a forward and a back, adding to his 2011 appearance as a number eight.
Scrum-half Greig Laidlaw captains a squad that has a total of 651 caps.
Three members of the squad – Alasdair Dickinson, Ross Ford and Sean Lamont – are set for their third tournament, while a further three – Richie Gray, Alasdair Strokosch and Richie Vernon – approach a second Rugby World Cup.
"We're very pleased to name the 31 and we're confident these players will represent Scotland well in the Rugby World Cup. It's been a tough but rewarding two months. We're proud of the effort everyone has put in to this point," said Cotter.
"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, however we must now move forward to our last preparation match against France before embarking on our Rugby World Cup campaign."
Scotland face France in Paris on Saturday in their final warm-up match before RWC 2015, where they are drawn with South Africa, Samoa, Japan and USA in Pool B.
After their opening match against Japan, Scotland will then travel north to Leeds to face USA at Elland Road on 27 September, followed by South Africa and Samoa on 3 and 10 October respectively at St James' Park in Newcastle.
"We felt the split of 17 forwards and 14 backs gives us the best balance," added Cotter.
"We have two games in four days followed by South Africa and Samoa, so we need to be robust and covered in both forwards and backs, while knowing we have players in the group who can play several positions.
"We'll now concentrate our efforts on this group to fine tune a couple of things in detail. There are fine margins in this sport at this level so we have to make sure we have got everything ticked off as best as possible, through our organisation, our work-rate and a raft of other details that we'll work through methodically.
"We know the Rugby World Cup is not far away, and we're very excited about the event, for which we're working very hard to perform, do well and represent the thistle on the world stage.”
Scotland RWC 2015 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.
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