The twin moves set the charge on a frantic day of talks between the players, manager Neil Lennon and chief executive Peter Lawwell.
Lennon has been tracking 23-year-old Griffiths since last summer, but had two previous bids in the region of £400,000 rebuffed this week by the League One outfit.
Today, though, as Griffiths arrived in Glasgow’s east end, it appeared the two clubs have settled on a fee.
Reports today said the deal would include £800,000 up front with add-on clauses amounting to a further £200,000.
As personal terms were being agreed with Griffiths, Ledley was heading back across the border after Celtic accepted an £800,000 bid from Palace for the midfielder who is out of contract in the summer.
Palace boss Tony Pulis sees the attacking midfielder as a vital element in his bid to keep the London side in the Barclays Premiership.
He had tried to sign the 27-year-old from Cardiff when he was in charge at Stoke before Ledley opted for a move to Celtic.
Ledley had refused to commit to a new contract and was a free agent in the summer.
Bracketed alongside Ledley was Greek star Georgios Samaras, who last night was reported to be on the wanted list of Turkish outfit Trabzonspor.
With their transfer business being dragged all the way to the wire, Lennon is happy to be able to reinstate Anthony Stokes to his attack for Sunday’s game against St Mirren following his two-game ban.
Despite the fact the 25- year-old has hit the net only seven times this season, Lennon has made it clear their efforts to sign another goalscorer does not automatically mean Stokes will be headed for the bench.
He said: “Stokesy is back this weekend, which is good. To be fair, before his suspension, in the games against St Mirren and then Motherwell, he was excellent.
“I just want him to add to his goals. I want him to keep that level of performance, and be more consistent with that.
“If he does this, he will play because he was excellent in both those games I mentioned.”
Even without Stokes for the games against Hibs and Kilmarnock, Celtic have thumped in 15 goals in their last four matches.
The spread of goals has delighted Lennon, who said: “Kris Commons has weighed in with a lot of those goals. But it is pleasing that everyone else is weighing in as well.
“We have been synonymous with good strikers over the years.
“That’s one of the reasons we went for Leigh Griffiths because he has got such a good goalscoring record, and he knows this environment very well.”
Suggestions that Beram Kayal could now be deemed surplus to requirements after the £2m purchase of midfielder Stefan Johansen in this window from Norwegian club, Stromsgodset, have been dismissed by Lennon.
The Israeli international has managed only 10 starts this season due to injury, and is now on the final lap of his rehab after breaking a bone in a foot at the end of November.
Lennon reported: “Beram will be another couple of weeks. And Steven Mouyokolo (who has been sidelined since rupturing an Achilles’ tendon in August), we are hoping will be another three to four weeks.”
The French central defender is desperate to get back into action, not least to try and secure another contract as the Hoops only signed him on a one-year deal last summer.
Lennon confirmed it is something which will have to be discussed, but added: “I have not spoken to him yet.”
Meanwhile, Dylan McGeouch has joined Coventry City on loan until the end of this season, where he will team up with ex-Celtic defender, Steven Pressley, who is manager of the League One club.