The pair were finally officially unveiled as Red Devils players and pictured in United shirts for the first time this week.
They arrived at the club's Carrington training base together on Tuesday as they met their teammates ahead of the new season.
Now the club have announced what numbers the pair will be wearing for the 2022/23 season.
Eriksen, who penned a three-year deal after joining as a free agent, will take the No.14 shirt.
It was vacated when Jesse Lingard left the club on a free transfer at the end of last season.
Aside from Lingard, the likes of Javier Hernandez, Alan Smith, Tim Howard, David May and the late Andy Goram have all worn the No.14.
Meanwhile, Martinez has taken over Paul Pogba's No.6 jersey for the new season.
Gary Pallister was the first to don the shirt on a regular basis before his departure in 1998, before Jaap Stam wore it for four seasons.
Wes Brown had possession of it between 2003 and 2011, before Jonny Evans and then Pogba took ownership.
There is perhaps an indication that United are keeping the No.21 shirt free for the time being, which was vacated by Edinson Cavani.
Eriksen wore that same number at Brentford, while Martinez also had it at Ajax for a number of years.
The No.21 happens to be the shirt number worn by Frenkie de Jong at Barcelona, who remains Erik ten Hag's top target this summer.