The left-back moves to Ibrox on a season-long loan.
Brentford director of football Phil Giles told the club's website: “Jayden had a positive pre-season and we have seen the benefits of a good loan move for him last season.
“The competition for places at full-back is very strong and we thought a loan might be the best way for him to develop this season. When this option came up, we thought it would be great for him.
“Jayden will be going into a high-pressure environment with the chance to compete for trophies and play European football. It is a great opportunity for him at a big club and I am sure he will relish it.
“We look forward to seeing how Jayden develops over the next year and welcoming him back at the end of the season.”
Meghoma has a deal with Brentford to 2028.