Laura Whittle, third at the British trials, joins compatriots Steph Twell and Eilish McColgan in the 5,000m.
Hammer throwers Mark Dry and Chris Bennett have also been granted selectors' picks for places in Rio.
It is the highest Scottish representation in track and field since the 1908 London Games, with GB sending an 80-strong team to Brazil.
Twell and McColgan were among eight athletes from Scotland who booked their places at the trials in Birmingham last month, with three marathon runners selected in April.
Just five Scottish runners made it to London 2012.
Team GB will be looking to improve on a haul of six medals from four years ago.
Scots in the GB athletics team for Rio 2016:
Callum Hawkins, Tsegai Tewelde, Derek Hawkins - marathon
Beth Potter - 10,000m
Andrew Butchart - 5,000m
Eilidh Doyle - 400m Hurdles, 4x400m Relay
Lennie Waite - 3,000m Steeplechase
Laura Muir - 1500m
Chris O'Hare - 1500m
Lynsey Sharp - 800m
Steph Twell, Eilish McColgan, Laura Whittle - 5,000m
Chris Bennett, Mark Dry - hammer

New City manager Pep Guardiola is keen to make Stones his next high-profile transfer of the summer.
Stones was one of only two outfield players not to see action in England's disappointing Euro 2016 campaign.
Talks have yet to take place, but the asking price would make Stones, 22, Britain's most expensive defender.
Everton have no need to sell, but the possibility is growing that Stones will leave before the start of the new Premier League season.
He was at the centre of a transfer battle last summer when Everton rejected a succession of bids rising up to almost £40m from Chelsea, simply refusing to sell to then manager Jose Mourinho.
Guardiola has made Stones, who has 10 England caps, a priority target as he prepares to renew his rivalry with Mourinho, who is now across the city at Manchester United, and looks certain to get his man.
Manchester City have already signed Ilkay Gundogan from Borussia Dortmund and completed a £13.8m deal for Spain forward Nolito from Celta Vigo after their interest in Euro 2016 was ended by Italy.
Everton will give any money they get for Stones to new manager Ronald Koeman to increase his already considerable transfer fund.
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Three more Scots have been added to the Great Britain Olympic athletics team, taking the total up to 15.
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Manchester City want to buy Everton defender John Stones, but would have to pay the Goodison Park club around £50m for the England international.