Sky Sports understands a number of clubs are tracking highly-rated Carlisle United midfielder Brad Potts.
Sheffield United are planning to send Andy Butler back out on loan after seeing an agreement with Walsall collapse.
The 54-year-old ex-Doncaster boss had been working as first-team coach at Nottingham Forest since January but has agreed to take over at Broadfield Stadium with immediate effect.
In a statement released by the club, O'Driscoll said: "I did a lot of due diligence on Crawley Town before I decided to accept the club's offer.
"I have been impressed with the owners and people behind the scenes and I am looking forward to helping the club establish itself in League One."
Craig Brewster assumed control of the side on an interim basis following Steve Evans' move to Rotherham, but remains on the coaching staff, while Steve Coppell continues in his role of Director of Football.
O'Driscoll added: "Crawley is a good fit for me. They are a club trying to do things the right way.
"I came to the club and the area three times before I decided to take the job and spoke to a lot of people.
"I got a very good feel for what has been achieved in the last two years and the potential there is to develop Crawley Town still further.
"This is a challenge I am really looking forward to. My football philosophy is to improve players and the way they think about the game. It is going to be a busy summer."