All Black prop McDonnell, who has won eight caps, has been recruited from Wellington and is the pick of the trio.
The 33-year-old front row, who weighs nearly 19 stone, will add beef to a pack that has proved underpowered this season.
He is joined up front by Bay of Plenty lock Sorenson, 27, who is a destructive ball carrier.
Samoa international Crichton, 30, has been lured from Super 14 outfit the Chiefs and can fill any position in the threequarter line.
Falcons director of rugby John Fletcher said: "This is a massive statement of our ambition and intent.
"All three players have been carefully selected over a period of time and will add a huge amount in key areas of the team.
"Credit has to go to the board and the chairman. We identified these three players as vital for the improvement of the squad, and they have gone out and got them for us."
Newcastle sit third from bottom in the Guinness Premiership following a disappointing start to the season.