Cole and Veron become Blues
Cole and Veron completed medicals at the club on Wednesday afternoon, and were officially announced as new signings on Wednesday evening.
Veron's £15 million move went through late on, but the Argentine player will now beat the Champions League deadline for registering players, and be eligible to face Zilina.
Veron and Cole could be joined by Christian Vieri from Internazionale, according to reports in the English media.
Board member Trevor Brooking defended the decision to sell Cole - pointing out that the fan-favourite could have left The Irons for nothing next summer.
"The fact was, a person who goes for nothing next year...you are ludicrous if you actually keep him from a business point of view," Brooking told Sky Sports.
"None of us wanted him to go. If we had stayed up, he probably would not have."
The Blues have been heavily active in the transfer market since Russian tycoon Roman Abramovich bought the club.
"Now my career has come full turn and I'm back at Chelsea," Cole told Chelsea TV after rejoining a club he had played for as a schoolboy.
"I'm really looking forward to it. I always give 100% and I'm looking to learn off the players here.
"First and foremost I have to get into the side, but I want to tell the supporters that I will always give 100% in every game."