On 1 February 2010, Slane signed a four-year contract with Celtic. He made his reserve debut in a 4–1 win over Queen of the South’s first team. Slane missed the entire 2010–11 season due to a cruciate ligament injury to his knee.
On 31 January 2012, Slane signed with English League One club Milton Keynes Dons on loan until the end of the season. Slane made his SPL debut for Celtic on Saturday 18 August 2012, as a substitute against Ross County. He was loaned to Scottish First Division club Partick Thistle in October 2012.