The 38-year-old Cole spent the last three seasons with the LA Galaxy of Major League Soccer, but was released following the end of the 2018 campaign.
Cole's contract with the club will run through the end of the current 2018-19 season.
“I’m delighted that we’ve been able to secure Ashley’s services for the rest of the season," Lampard said in a statement.
“He’s a fantastic player, a quality left-back, and he also brings great experience to the dressing room.
“I know him very well from our time together at Chelsea, and with England, and I also know what he can bring to the group and the influence he will have."
Lampard also praised Cole's condition despite not having played since the end of the MLS season, but did not promise the veteran left-back will be given a place in the squad.
“Ashley is in good shape, which doesn’t surprise me because he’s an excellent professional, and he will compete for a place in the side like every other player here.
Cole returns to England for the first time since 2014, when his time at Chelsea came to an end.
He originally came up through Arsenal's youth system and spent the first seven years of his career featuring for Arsenal under Arsene Wenger, before making his controversial move to Chelsea prior to the 2006-7 season.
He would also play alongside his England team-mate Lampard with the Blues, doing so in the Premier League 190 times – more than he did any outfield team-mate with Chelsea.
He had a successfull three-year spell in Los Angeles with the Galaxy after that, though the 2018 season ended in disappointment as the club missed the MLS postseason and decided to not bring back Cole for another season.
Instead, he will turn his focus toward helping the Rams back to the Premier League for the first time since 2007-08.
First-year manager Lampard has his side sixth in the Championship, in the last of the promotion playoff spots, seven back of Norwich in second and two points ahead of Bristol City.
The club is next in action in the FA Cup on January 29 against Accrington Stanley, before returning to Championship action February 1 against Preston.