The publisher, which also produces magazines for Holland & Barrett and Superdrug, beat a number of other unnamed rivals in a pitch.
McDonald's is reluctant to talk about its plans although the title is expected to be quarterly. It will be available from the restaurants and targeted at mothers.
Nick Hindle, the head of corporate affairs for McDonald's, admitted the company was looking at ideas with River, but said nothing had been confirmed.
"Mums are a really important audience for us so it seems logical to explore that," he said.
The magazine would help reverse negative perceptions brought on by rising concerns about child obesity and the release of the Morgan Spurlock film Super Size Me last year.
McDonald's has introduced an alternative menu including a salad range, fruit and healthier breakfast options.