Beattie has agreed a three-year deal and will join from West Brom for a club-record undisclosed fee while Trundle, a cult hero in South Wales following a previous spell with the Swans, has joined on loan from Bristol City until January 1.
The pair's arrival is a timely boost for manager Paulo Sousa, who is currently without a number of first-team players.
Leading scorer Stephen Dobbie is out with a hip injury while captain Garry Monk, defender Angel Rangel and striker Gorka Pintado are all suspended following their dismissals in Tuesday night's Carling Cup defeat to Scunthorpe.
Another new striker, Besian Idrizaj, is struggling with a thigh strain but Joe Allen (hamstring), Ferrie Bodde (knee) and Fede Bessone (groin) are nearly fit.
Darren Pratley (shoulder) and Thomas Butler (hernia) are definitely out.