Swanson comes into the squad after Celtic captain Scott Brown was ruled out with an ankle injury.
There is no place for Hibernian striker Garry O'Connor, who took his goal tally for the season to 10 with a double against St Johnstone last night, or his former Easter Road team-mate Steven Fletcher.
Fletcher recently claimed he had not made himself unavailable for selection despite asking not to be considered for the Carling Nations Cup tie with Northern Ireland in February, but his exile continues.
Scotland manager Craig Levein bought Swanson from Berwick while United manager and has called him the most talented player he has worked with.
The 24-year-old would have been in earlier squads but missed out through injury, but has recovered from early-season fitness problems to net in each of United's last two Clydesdale Bank Premier League games.
Brown is out with the ankle injury he first picked up in Scotland's friendly win over Denmark in August, with Celtic manager Neil Lennon fearing he faces more than a few weeks on the sidelines.
Levein has made three changes in all in his 25-man squad for the games in Vaduz on October 8 and against the world champions in Alicante four days later.
Cardiff goalkeeper David Marshall comes in for Preston's Iain Turner while Middlesbrough defender Stephen McManus returns to the squad. Liverpool centre-back Danny Wilson has dropped out.
Swanson is unlikely to start either game but Levein is keen to have him involved with the squad.
He said: "I've tried to get him into the squad on numerous occasions but he has been injured.
"I believe he fits the profile of the type of football we are trying to play.
"I think he will be a valuable addition to the squad. I don't expect him to start any of the matches but it's good to finally get him into the squad to see what it's all about."
On the absence of Brown - who is out with an ankle injury - Levein said: "He is such an infectious character and started the season well.
"Unfortunately he is injured and we don't have him and he's not available.
"There are other players more than capable of stepping into Scott's shoes."
Hibs striker O'Connor was left out of the squad as a result of off-field issues and is to stand trial next year accused of possessing cocaine.
Levein said: "The reason Garry isn't involved in this particular squad is that he has other issues to deal with just now off the field.
"Once he has those clear and out of his mind it would allow him to concentrate completely on football.
"I have made Garry aware that he is very much in my thoughts and if he continues in this fine vein of form then he will be included in the squad."
Scotland squad: Gilks (Blackpool), McGregor (Rangers), Marshall (Cardiff); Bardsley (Sunderland), Berra (Wolves), Caldwell (Wigan), Crainey (Blackpool), Hanley (Blackburn), Hutton (Tottenham), McManus (Middlesbrough), Whittaker (Rangers); Adam (Liverpool), Bannan (Aston Villa), Cowie (Cardiff), Dorrans (West Brom), Fletcher (Manchester United), Forrest (Celtic), Morrison (West Brom), Naismith (Rangers), Robson (Middlesbrough), Snodgrass (Leeds), Swanson (Dundee Utd); Goodwillie (Blackburn), Mackail-Smith (Brighton), Miller (Cardiff).