Elliot’s arrival was announced four hours after the club confirmed that former Blackburn, Manchester City and Stoke City boss Hughes had left.
Chairman Tom Piatak said in a statement that they were “grateful for the work he has done, the standards he brought and the progress made during the season”.
“Following open and respectful discussions, both parties agreed this was the right time for the club to move in a different direction,” he added.
Former Newcastle goalkeeper Elliot initially took over at Gateshead in a caretaker capacity in September 2023 after Mike Williamson left for Carlisle.
He led the Tyneside outfit to sixth place but they were unable to compete in the play-offs because their ground did not meet the entry criteria for membership of the EFL.
Elliot joined then-League One Crawley in October 2024 but was sacked the following March with them 22nd in the table after six wins from his 33 games in charge.
He returned to Gateshead in January with the side in dreadful form at the foot of the fifth tier and they were then 11 points adrift by the middle of the following month.
However, after ending a run of 13 successive league defeats on 17 February they then lost just two of their final 15 matches to finish eight points clear of the relegation zone.
