Three of his six BetSid stores have been bought by an independent Preston bookmaker.
But the remaining three have closed their doors and will not re-open. Up to nine members of staff will be made redundant.
The shops in Friargate, Preston, Buckshaw Village near Chorley and Clifton Street, Lytham were shut down over the weekend.
Today Mr Rigby pledged to honour all bets placed there, with punters advised to cash their winning betting slips at one of the three which are remaining open - Church Street, Preston, New Hall Lane, Preston and Market Street, Chorley.
"The most important thing to stress is that all bets will be honoured by the new owners," he told the Post.
"The sale is really a management buy-out, because the owners of Place Your Bets have been working as part of my management team for a while now.
"It is certainly much better in the hands of local lads who have been running local bookmakers. Three of the six shops have shut and the other three are trading as normal. It's business as usual."
Accounts show that BetSid has been operating at a loss since it was first launched in May 2013.
Mr Rigby has been keeping the company running from his own pocket during that time and at the end of 2017 it had already cost him more than £2.1m.
In a statement announcing the deal, the entrepreneur said: "The Rigby Organisation is delighted to announce that it has agreed the sale of BetSid to Place Your Bets Limited.
"The disposal of BetSid is part of Rigby Organisation's strategy to concentrate on being a landlord and not an operator. But this disposal goes beyond us simply disposing of a non-core business."Bookmaking is going through a period of great change in the first half of this year. Industry experts say over 4,000 shops will shut as a result of changes in legislation.
"In order to survive such change I believe that BetSid is better part of a business focused entirely on high street bookmaking."