The couple - who split in November after a 10-month romance - recently reunited and the besotted boy band star has showered The Saturdays singer with expensive gifts to celebrate, including the designer accessory and a handcrafted silver eternity ring.
A source told the Daily Mirror newspaper: "When they split up, both parties were utterly miserable.
"They went for a private drink a couple of weeks ago and decided to give their relationship another shot. After presenting her with the bag and eternity ring, smitten Marvin suggested they think about moving in together.
"As far as romance is concerned, it is full steam ahead."
'One Shot' singer Marvin, 25, also wooed his love as his group performed a concert at London's The O2 venue last weekend. He sang a song just for Rochelle, even heading over to her seat to serenade her.
The pair initially split because work commitments with their respective groups prevented them from seeing each other.
Marvin explained in November: "I'm on tour for two months and then as soon as I come off, she's on tour for six weeks. We're both very sad. It was a very tough decision but we truly believe - both of us - it's the best for right now."
He also added at the time that they had not ruled out a reconciliation and he felt they were "right for each other".