Centre-back Anderson, 27, has cancelled his Barrow contract by mutual consent to join their National League rivals.
The ex-Aldershot and Exeter player, who has also played in Italy, could feature against his old club on 18 February.
Striker Keating, 21, was recommended to Gulls boss Kevin Nicholson by ex-Port Vale manager Micky Adams.
He has previously had spells with Sligo Rovers, Galway United and Finn Harps, with his move subject to international clearance.
"Myles hasn't played a huge amount of games for a 27-year-old, but he is the stature, the voice, and is the leader-type I've been after." Nicholson told BBC Radio Devon.
"Ruairi is young, a little bit raw, but incredibly hungry to show what he's about."
The Gulls are currently four points above the relegation zone, and have won only one of their last six games.
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Torquay United have signed Barrow defender Myles Anderson on a permanent deal, and Irish forward Ruairi Keating on non-contract terms.