The Sun's source went on to surmise why the pair chose a quiet celebration rather than a lavish do.
"Despite living in the spotlight, Rita is determined to keep the relationship as private as possible and didn't want to make a big song and dance about the wedding," they said, adding that there are plans for a "big, showbiz-style bash" to celebrate their union in time.
However, they told The Sun fans shouldn't expect to see it "being flogged to the highest-bidding magazine".
It also appears there won't be a honeymoon any time soon with Ora reportedly busy recording new music.
Waititi and Ora confirmed they were in a relationship last year, with rumours persisting in recent months that the couple were engaged.
Waititi has been seen on Instagram recently holidaying with Ora and his two children from his previous marriage to New Zealand film producer Chelsea Winstanley.