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Both players, who have impressed many with their performances this season, were expected to sign back in January but talks were held up by former manager Colin Lee's departure from the club.
Defender Craig is expected to sign tomorrow while May is set follow early next week.
"I have loved every minute of my time at Millwall", Craig told the South London Press. "Playing regularly makes it so much sweeter.
"Millwall gave me my first chance as a professional, which I really appreciated and I always wanted to stay. I am very pleased to have sorted out a long deal and hopefully now, I can help us beat the drop to put the icing on the cake."