Catalysis of the reaction: 10-formyltetrahydrofolate + N1-(5-phospho-D-ribosyl)glycinamide = tetrahydrofolate + N2-formyl-N1-(5-phospho-D-ribosyl)glycinamide.
10-formyltetrahydrofolate:5\'-phosphoribosylglycinamide N-formyltransferase activity