Elphick, 30, leaves Villa for a second loan spell this year, having joined Reading in January. Martin also signed on with Reading at the beginning of 2018 and the pair will reunite at Hull this term.
"Hull City have signed experienced defender Tommy Elphick on loan from Aston Villa until the end of the 2018/19 season," the Tigers announced on Friday.
Regarding Martin, they said: "The 29-year-old has joined Hull City on a season-long loan and will be eligible to make his debut when the Tigers face Ipswich Town at the KCOM Stadium after the international break, as he is unable to play against his parent club this weekend."
“I’m excited about a new challenge and to be working for Nigel Adkins and with this group of players," Elphick told the club's official website.
Martin added: “I can’t wait to get started here after having a really positive chat with the Head Coach.
“Hopefully I can come here, play regular football and contribute towards helping the team to move up the table. I’m fit, fresh and ready to play as many games as possible.”