Burgic, 24, was top scorer in the Slovenian league last season and had attracted interest from Big Sam, as he searches for that elusive 20-goal-a-season striker.
"Many clubs were after me, but they didn't show enough will to sign me," Burgic said.
"I admit, Bolton watched me a couple of times. I don't know if they were in talks with my former club.
"But I know Nantes were. They agreed everything with Gorcia but we just had to agree personal terms.
"I'm not unhappy or anything like that. Of course it would be nice to play for such a big club as Bolton, but I'm sure I will get more chances to prove myself at AIK.
"I am still very young and I believe that one day I will be playing in England or France.
"But I was just sick and tired of waiting. AIK's offer was good, I was happy with everything so I signed."
Meanwhile, Bolton full-back Nicky Hunt could be fit for the start of the season after an injury scare.
Manager Sam Allardyce said: "Nicky should be okay to return to playing in two to three weeks."