The National Lottery Commission has launched the competition for the licence to run the lottery for 10 years from February 2009.
There were 257 million winning lottery tickets last year
The third licence has been extended from seven years to encourage bidders.
Eight competed for the lottery's first licence - but the second drew bids only from current operator Camelot and Richard Branson's People's Lottery.
Bids, which cost an estimated £5m to £10m to prepare, are now expected from the UK and abroad, the commission said.
It has published its Statement of Main Principles, setting out a series of "hurdles" contenders must pass.
They must prove they have the full operational, financial and technical capability to run the lottery and manage a 20-month transition period - between the licence being awarded and coming into effect - without any interruption to service.
The contenders will then be judged on the predicted amount of money they will raise for the Good Causes fund.
A spokesman for Sir Richard Branson said he would now decide whether to bid again.
He was intending "to ensure that the maximum amount of money goes to Good Causes and that there is a feel-good factor about the Lottery, which certainly does not exist at the moment", the spokesman added.
A Camelot team has been working on its bid since the beginning of this year.
Commission chief executive Mark Harris said: "We are impartial as to the identity of the next licensee.
"The best bid will win."
The regulator is now working on a draft "invitation to apply" to be issued in April 2006.
Bids will be accepted between October 2006 and January 2007.
Equipment and software suppliers, retailers and contractors will be allowed to back more than one bidder.
If Camelot fails to win the licence, its successor will have the option of taking over the existing lottery terminals for a minimum price of £10m, the commission said.
The terminals could also be used for utility-bill payments - providing these raise some money for Good Causes.
The licence winner will also have to raise an extra £750m for the 2012 Olympics.
The lottery has contributed more than £17bn to Good Causes and paid out more than £25bn in prizes - making 1,700 millionaires.
Camelot's pre-tax profits for the last financial year were £47.5m, the commission said.