Camp, 31, has penned a two-year deal in South Yorkshire following his release from Bournemouth while Andreu and Odjidja-Ofoe both join on loan from Norwich, with all three deals announced after the 6pm deadline.
Andreu will stay until January and Odjidja-Ofoe has penned an initial one-month emergency loan. Both men played against the Millers in last week's Capital One Cup clash at New York Stadium.
Camp's arrival shows commitment by boss Steve Evans to address his goalkeeping department.
The Northern Ireland international, who was formerly represented England Under-21s, looks set to become the Millers' number on, with Evans sending on-loan flop Kelle Roos back to Derby, while appearing to have little faith in established stopper Adam Collin.
Meanwhile, Evans is excited by the capture of the Norwich pair.
Odjidja-Ofoe played 90
minutes last week and impressed while Andreu came off the bench and both men
chose the Millers over other clubs.
“Both lads
have been on my radar for some time and I am again delighted that despite a lot
of interest in securing them we have brought them to Rotherham United,” Evans
said.
“Tony
Andreu is a very talented player, one who has a superb goalscoring record. He
is a player who can play as a main striker or indeed one who supports a lone
striker or two.
"He
is always looking to be creative in the final third of the pitch whilst he
retains a self discipline to work extremely hard for the team.
“Vadis is
an exciting talent and a player we look forward to working with, he is a full
Belgian international. In last week's Capital One Cup match here versus
Norwich City this lad was by far the best player on show.
"Our
supporters who attended that evening will recall his dynamic movement, his pace
and power and undoubted technical ability."
