It was also announced that England manager Louise Ramsay has accepted the role of Lions team manager for the tour.
Woodward's appointment is no surprise given England's recent achievements, while Beaumont, England's 1980 Grand Slam captain, was always a clear favourite for the manager's role.
"I am delighted to accept the job of head coach to the 2005 Lions," said Woodward.
"It is a huge honour to play for the Lions, and to be given the opportunity of taking the squad to New Zealand is a huge challenge and one I want everyone connected to the squad to enjoy."
Woodward added: "Louise's appointment was part of my agreement to accept the job as head coach, and her role is a crucial one to the success and smooth running of the tour.
"Although my direct involvement with the Lions doesn't start immediately, the work relating to the essential logistics and the administrative related aspects of the tour has to start now.
"There will be a lot of speculation about our itinerary and other coaching and managing appointments for the tour, but I am sure people will understand that I will only comment further on the Lions appointment once the RBS 6 Nations Championship has been completed."
Beaumont, who is also chairman of the Lions, said: "It will be a privilege to work with Sir Clive Woodward, who is the head coach and responsible for all rugby matters. He has an outstanding record, and I know he is looking forward to the challenge."
RFU president Robert Horner said: "On behalf of everyone in the game in England I wish most warmly to congratulate Clive on his appointment.
"It is a tribute to Clive and all that he has achieved in the last six years with England, culminating in the RWC victory against Australia last November and I wish him every success in New Zealand in 2005."
RFU chief executive Francis Baron said: "I'm delighted that Clive has been awarded the honour of coaching the British Lions.
"His commitment and immediate priority is of course England in the RBS 6 Nations. However I know he is looking forward to the challenge and he will do an excellent job."