Both players are Scotland A internationals and have agreed two-year contracts, with 23-year-old De Luca returning to the club he served as an apprentice last year.
De Luca's decision to return to Edinburgh was welcomed by backs coach Rob Moffat, who said: "I think his time at the Borders has been good for his development as his rugby is maturing and although he is still a young, developing player, he is capable of playing in Europe and the Magners League."
Grant has been serving in the Royal Signals but becomes a full-time professional, and said: "It is a positive move for me, to be able to play alongside some big names at Edinburgh such as Allister Hogg, and learn from Allan Jacobsen, so I am really looking forward to next season."
