Donnelly made his Cliftonville debut on 7 September 2010, coming on as an 85th-minute substitute in a 2–0 defeat against Linfield at Windsor Park in the County Antrim Shield. He went on to make 33 league and cup appearances in the 2010-2011 season, scoring 7 league goals. The 2011-2012 season started well for Donnelly.
His good form. continued, and he scored 13 goals in his first 18 league games of the 2011-2012 season to attract interest from Arsenal and Liverpool, with the latter club"s manager, Kenny Dalglish, confirming they had registered their interest.
Donnelly made his final appearance for Cliftonville on 17 December 2011, in a 2–1 home defeat against Coleraine. He had scored a total of 22 goals in 54 league and cup appearances spanning two seasons.
In December 2011, Swansea City offered £100,000 for Donnelly, before Everton bid "considerably more". The Welsh club then upped their bid and Donnelly agreed a three-and-a-half-year deal with Swansea on 30 December 2011 for an undisclosed fee.
The transfer was completed on 10 January 2012, and Donnelly was given the shirt number 41.
Donnelly scored on his debut for the reserves in an 2–2 draw with Chelsea reserves at Parc-y-scarlets on 28 March 2012. Donnelly made his first senior appearance for Swansea in a League Cup fixture against Crawley Town on 25 September 2012, coming on as a substitute for Michu. His full début came the next season in a Europa League play-off against Petrolul Ploiești which ended in a 2–1 defeat.
On 28 May 2015 Swansea City confirmed that Donnelly had been released by the club
= Coventry City (loan) On 31 January 2014, Donnelly joined Coventry City on loan until the end of the 2013-2014 season. On 4 February 2014, it was confirmed that Donnelly had returned to Swansea City due to non-footballing personal reasons.
= Tranmere Rovers (loan) On 6 February 2015, Donnelly was named the League Two Player of the Month for January after scoring 3 goals in his first month at the club, taking Tranmere Rovers out of the relegation zone. In November 2011, he was called up to the Northern Ireland Under-21"s for the first time, but he did not feature in the match against Serbia.
In June 2013, Donnelly informed the IFA that he did not wish to be considered for selection for Northern Ireland.
However, he then made his Under-21 debut against Denmark in September 2013.