The 25-year-old is currently a free agent after leaving Kenilworth this summer following two injury-hit seasons at Luton, playing just six times in total after being signed by former Town boss Graeme Jones.
However, the one-time England U21 international, who was called up to the Zimbabwe squad for their World Cup qualifiers against South Africa and Ethiopia later this year, will now spend pre-season at Home Park.
"I have known Brendan since he was a kid at MK Dons.
"He's a fantastic lad, he has had a couple of injuries over the years.
"We want to give the lad an opportunity to earn a contract, so we are pleased to have him on board and have him with us.
"If he does well and gets through the training schedules, which are intense, then hopefully we can see Brendan Galloway in a green shirt."