The SPL confirmed earlier on Monday that Dundee would be 'Club 12' - a spot left empty in the league following the rejection of newco Rangers into the top flight last week.
Dundee finished second in the Irn-Bru First Division last season and were one of two clubs in with the chance of playing in the SPL in the upcoming season.
The other side was Dunfermline, who finished bottom of the SPL last season, but Gardiner told Sky Sports News he always believed Dundee were the preferred option.
"We were always confident that on sporting merits it was an open and shut case - however it is obviously extraordinary circumstances just now and so you could never be sure of anything," he said.
"I received a call just prior to the SPL releasing their confirmation of it. Once again I can assure you that we will be accepting the invitation."
Gardiner was also relieved that the club can now start to prepare fully for the season now they know which league they will be playing in.
"We haven't been able to take a breath yet, let alone a sigh of relief," he said.
"We have kind of been in limbo, certainly for a few weeks and only now can we start to plan properly for the SPL."
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