Penrose was born in Ballynacargy, County Westmeath, and educated at St. Mary's CBS, Mullingar; Coláiste Mhuire, Mullingar; Multyfarnham Agricultural College; University College Dublin (UCD), and the King's Inns. At UCD, he studied Agricultural Science, graduating in 1979 with a bachelor's degree and after graduation, with a colleague, formed an agricultural consultancy firm in Mullingar. In 1986, Penrose took up the position of advisor to the Minister of State at the Department of Fisheries, Forestry and Tourism, Michael Moynihan, resigning from the agricultural consultancy to do so.
In 1984, Penrose was co-opted on to Westmeath County Council, and a year later, he ran in the local elections, winning his seat in the Mullingar Lough Owel constituency by a margin of just six votes. In the 1991 local elections, he topped the poll in the Mullingar Rural Area.
He qualified as a barrister in 1990 before entering into national politics. At the 1992 general election he was first elected to Dáil Éireann as a TD for the Westmeath constituency. On that occasion the Labour Party won a record 33 Dáil seats, a feat that was surpassed at the 2011 general election.
In 2002, Penrose was a candidate for the deputy leadership of the Labour Party. Although he was part of a joint ticket with Pat Rabbitte, who won the leadership comfortably, he was narrowly defeated for the deputy leadership by Liz McManus, polling 1,636 votes to McManus' 1,728.
On 10 March 2011, he was appointed as Minister of State for Housing and Planning.
On 15 November 2011, he announced his resignation as Minister of State due to his opposition to the Government's decision to close Columb Barracks in Mullingar. Penrose said: "I understand and appreciate that significant efforts were made by my Labour colleagues in Government, who fully understood the depths of my feelings in this regard, to resolve this matter, but to no avail." He also resigned the Labour parliamentary party whip.
In February 2012 the Phoenix magazine contrasted Penrose who "eats at the PLP tables in the Dáil restaurant and is often seen chatting to Gilmore on the corridors" with two other backbenchers who lost the party whip, Tommy Broughan and Patrick Nulty, both of whom had been "banished" from the Labour parliamentary offices.
Penrose rejoined the parliamentary Labour Party in October 2013. He was narrowly re-elected to the Dáil at the 2016 general election, the final of just seven Labour TDs returned.