The "Russian Roulette" singer delighted the 25-year-old Los Angeles Dodgers baseball star when she suggested he came to live in her Hollywood mansion, just months after they started dating.
A source said: "Matt is very happy to be moving in with Rihanna."
"He knew it was only a matter of time before Rihanna moved him in. He wants to make her happy."
"He had boxes of his things brought over in mid-March. He's training in Arizona now, but when he's back he'll be at her place."
However, Matt is said to be being cautious about the move and is not currently planning to put his own Los Angeles property on the market.
The insider told America's Star magazine: "He's keeping his house, to see how things go. But they are so in love."
Rihanna and Matt - who were first romantically linked in January after they holidayed together in Mexico - have always played down their relationship and claimed they are "just friends."
However, the sportsman recently introduced the 22-year-old singer to his family when she attended an Ante Up for Autism charity fundraiser he was involved with.
A source said: "Matt was happy she came. It was an awesome show of support. Rihanna fit right in as if they all knew each other. It was comfortable."
