After being released by Brentford, Shay signed a pre-contract permanent move with Aberdeen on a two-year contract on 27 May 2014.
Logan’s first appearance after signing for the club on a permanent basis came against FK Daugava Riga in the first qualifying round of the Europa League, during which he scored the opening goal, in a 5–0 home victory. In the second leg, Logan then provided an assist for Adam Rooney, who went on to score a hat-trick, in a 3–0 win over to send them through to the next round. However, Aberdeen’s Europa League run came to an end after losing 5-2 to Real Sociedad on aggregate, during the second leg Logan gave away the penalty which allowed Real Sociedad to equalise.
On 13 September, in a match against Celtic, he complained of racist abuse from opponent Aleksandar Tonev, who was found guilty and given a seven-match ban. Following the verdict, Logan said he forgave Tonev’s actions against him. Logan scored his first league goal for Aberdeen on 27 September 2014, in a 3–2 win over Inverness Caledonian Thistle. On 10 November 2014, at full time of Aberdeen’s 2–1 defeat to Celtic, Logan received a red card for using “offensive and insulting language”, resulting in a one-match ban. During the season he went on to score goals against St Mirren and Ross County. With Aberdeen challenging at the top of the league, Logan stated his belief that the club could win the Scottish Premiership. He helped the club finish in second position, qualifying for a European place. Not only that, Logan was named in the PFA Scotland Premiership Team Of The Year on 1 May 2015. In his first season at Aberdeen made 45 appearance and scoring four times in all competitions.
Ahead of the 2015–16 season, Logan was linked a move back to England, with Bolton Wanderers. In April 2016, he signed a new contract, keeping him at the club until summer 2018.