Committee chairman Keith Vaz said he was "looking forward" to hearing from Mr Winsor, with whom he has clashed during previous hearings.
Bridget Phillipson, Labour MP for Houghton and Sunderland South, said she was "stunned" by the decision, saying she could not even believe reports that Mr Winsor had applied.
Matt Cavanagh, of the Institute for Public Policy Research (IPPR) think-tank, said he was a "risky if not reckless choice" which could damage the reputation of Her Majesty's Inspectorate of Constabulary (HMIC),
"As well as putting the relationship between Government and the police under further strain, this provocative choice could put at risk the growing reputation and contribution of HMIC at a crucial time."
Mrs May was heckled, booed and jeered at the federation's annual conference in Bournemouth last month, just a week after some 30,000 officers marched through central London in protest over Mr Winsor's proposed reforms, most of which have been accepted.
He called for the current police pay system, based on a 1920s model of rewarding years of service, to be overhauled and replaced with one that recognised hard work and merit instead.
Among the more controversial proposals in his two reports, Mr Winsor recommended that police constables' starting salaries should be cut by up to £4,500 and that the retirement age should be raised to 60.
He also proposed scrapping a series of allowances and special payments intended to save £60 million a year overtime.
Officers on frontline duties would see their pay rise but 40% of officers who do not work unsocial hours face cuts of up to £4,000 a year.
Mr Winsor also signalled the end of a job for life as he called for the ban on Chief Constables making officers redundant to be lifted in the face of budget cuts.
He has been put forward by the Home Office to replace Sir Denis O'Connor, who retires at the end of next month, overseeing the functioning and performance of police forces.
A Home Office spokesman said: "Tom Winsor has been named as the preferred candidate for the role of Her Majesty's Chief Inspector of Constabulary."
Mr Winsor was the rail regulator from 1999 to 2004 when he joined White & Case's energy, infrastructure, project and asset finance practice in its London office.
In that role he carried out two major reviews of the structure and level of charges for the use of the national railway infrastructure.
Sir Denis is retiring after more than three years in the HMIC role.
When his retirement was announced in March, Mrs May said he had been "invaluable in enabling the inspectorate to continue to deliver an efficient and independent inspection programme during many challenges and changes in the policing landscape".
