Strachan left the club after 12 months in the job and Boro has confirmed that no compensation was paid.
“It is a sad day, Gordon worked very hard for the club, but he would be first to admit things have not worked out as we hoped,” said Gibson.
“Today Gordon met with me, we had a long discussion and in that debate he offered his resignation and I accepted it.
“He is a man of massive integrity, very hard-working and cared deeply for this club. We gave him many sleepless nights and I know he gave it his best, but sometimes circumstances dictate that it just doesn’t work.
“Gordon is a rare guy, I like him enormously, but it just didn’t work and the integrity he has shown made life very easy for me.
“He tore up his contract and sought no compensation, he walked away from the club with empty hands. He left without any compensation whatsoever.
“We felt it was in the best interest of the football club at this time, he didn’t need to be shoved – he walked.”