According to the BBC, SPL clubs also agreed that it would "work with the Scottish FA, SFL and Rangers to facilitate Rangers FC taking their place in SFL Division Three".
The SPL fixtures had left space for a "Club 12" after the old Rangers headed for liquidation.
SPL chief executive Neil Doncaster said the decision had been taken "purely on sporting integrity" and that Dundee were the "overwhelming" choice of the other clubs.
Dundee, who were runners-up in Division One and finished 24 points behind champions Ross County, will accept the invitation to play in the SPL.
Dens Park chief executive Scot Gardiner said: "We were always confident that, on sporting merit, it would be us, but we have been in limbo for a few weeks and, only now, can we start to plan properly for the SPL.
"We have a very good squad of players and can now add to that squad."
With Dunfermline unlikely to challenge the decision, Dundee, who were themselves in administration two years ago, will now start the SPL season away to Kilmarnock on 4 August.
The new Rangers are expected to start their new life by taking the Dens Park side's place in the first round of the Ramsdens' Cup.
Dunfermline were hoping East End Park will continue to house SPL games
Charles Green's Sevco consortium will hope the new Rangers will be accepted as SFA members this week and they are now due to travel to face Brechin City, who were expecting to face Dundee, on 28 July.
Airdrie United, who were runners-up in the end-of-season play-offs, will replace Dundee in the First Division, with Stranraer moving up a division to take Airdrie's place.