The lawsuit is a fresh blow to the reputation of the fire alarms to medical equipment giant.
Its ex-chief executive, Dennis Kozlowski, stepped down earlier this month shortly before being indicted on tax avoidance charges; the US stock market regulator is also looking into Mr Kozlowski's affairs.
In its suit against Mr Walsh, Tyco alleges he solicited, and received, the fee from Mr Kozlowski after recommending the purchase of the CIT financial services business to Tyco's board.
'Overreaction'
Tyco's filing says that Mr Walsh did not declare the fee to the board and that when it came to light and he was asked to return it, he refused.
The filing was made to the US District Court in Manhattan.
Mr Walsh has issued a statement saying the lawsuit "is clearly an overreaction to the recent and well-reported problems and management changes at Tyco."
He said he made the deal "at the direction of then-CEO Dennis Kozlowski...I put my more than 30 years of deal-making experience to work and helped to bring the transaction to a successful conclusion."
Furthermore, he said, the fee consisted of two $10m payments, one to himself which was disclosed, and one to a New Jersey charity to which he is an advisor, "but not a trustee with any active control of the funds."
Choppy water for float
The filing comes less than a week after Tyco got the go-ahead from the US stock market regulator, the Securities and Exchange Commission, to sell shares in CIT.
Debt-burdened Tyco expects to raise about $5.8bn from the flotation of CIT, which has been pencilled in for early July.
News of the flotation sent Tyco's stock up more than 35% on 13 June.
The SEC has begun a preliminary inquiry into Tyco. The firm's new chief executive, John Fort, has told shareholders that this SEC inquiry relates solely to Mr Kozlowski.
The SEC has not commented on the inquiry.
Mr Kozlowski, the man behind the creation of Tyco, was charged with avoiding $1m in New York state sales taxes on purchases of artwork worth $13m.
Prudential Securities analyst Nicholas Heymann said the charges against him would prompt "a more aggressive review of all of the company's operating policies."