Finnigan was born in Jarrow, Tyne and Wear.[4] As a youngster, he played for Jarrow F.C.'s under-age teams before joining Newcastle United.[5] He scored 56 goals for Newcastle's reserve and academy teams from 102 starts and 20 substitute appearances, but never appeared in a competitive first-team game.[6]
Finnigan joined Scottish Premier League club Falkirk on 23 January 2007, replacing Anthony Stokes who had left the "Bairns" to sign for Sunderland.[5] He made his Falkirk debut, and his first appearance in a senior league, as a second-half substitute against Kilmarnock on 27 January 2007.[7] The forward scored his first Bairns' goal three weeks later against Rangers, when he "played a neat one-two with Gow and drilled a shot beyond McGregor from the edge of the penalty area".[8] In the 2008–09 season, he played a major role, scoring twice and winning a penalty, in Falkirk's 4–0 victory over rivals Inverness Caledonian Thistle in what proved a successful fight against relegation.[9] He also scored the winner against the same opposition to take Falkirk through to the semi-final of the Scottish Cup,[10] and had a goal disallowed in the Cup final.[11] Before the 2009–10 season, Finnigan signed a new one-year contract with Falkirk, with an option for a second year.[12]
On 24 June 2011, Finnigan signed for Scottish Premier League (SPL) club St Johnstone.[13] In February 2012, Finnigan signed on loan for Dundee.[14] He scored on his debut for Dundee, a late equaliser in a 1–1 draw with Falkirk after coming on as a second-half substitute. Finnigan then scored in a 3–2 win over Livingston. Finnigan returned to St Johnstone in April 2012 following a season-ending cartilage injury, but then signed for Dundee on 1 June.[14]
In August 2013, Finnigan joined South African National First Division side Chippa United on a one-year contract.[15] He scored on his debut on 6 October 2013 in a 1–1 draw with Thanda Royal Zulu[16] and went on to score a total of 4 goals in 9 league appearances.[17][18]
On 11 September 2014, it was announced that Finnigan had signed for Gateshead until the end of the season subject to international clearance.[19] He made his debut on 20 September as a half time substitute against Welling United, scoring the equaliser in a 1–1 draw within 5 minutes of coming off the bench.[20]
On 2 July 2015, Finnigan signed for Township Rollers of the Botswana Premier League scoring 9 goals within 21 appearances.[21]
On 26 August 2016 he signed for South Shields.[22] The club went on a 42-game win streak, getting promoted to the Northern Premier League Division One North and winning 4 trophies in one season.
On 23 May 2019 it was confirmed that Finnigan had joined Whickham.[23] On 14 December 2019, he was loaned out to Morpeth Town for the rest of the season,[24] and joined them on a two-year contract ahead of the 2020–21 season.[25]
After seven months out with health issues, Finnigan joined Dunston UTS in September 2022.[26]