With Antonio Conte having previously revealed that he took the decision to part with the Spain international back in January, it has taken eight months for the Blues to push a move through.
The summer transfer window came and went without any movement, with Costa forced to take matters into his own stands as he went AWOL in Brazil and accused Chelsea of treating him like “a criminal”.
He has now got his wish, with Atletico free to register him for a second spell in January, and Blues legend Lampard believes the agreement makes sense for all concerned at the end of a long-running and potentially disruptive saga.
The former England international wrote in a column for the Evening Standard: “Costa leaving will be a relief to Conte and Chelsea - it is the best thing for all concerned.
“If it was just a case of selling a talented striker, then we’d be talking about what a great loss he is to the club. But he had to go. There was no way he could stay at Chelsea, given the events of the summer and the sooner he went, the better.
“It’s great for Costa, too. He needs to go and train properly before starting playing again in January. He couldn’t carry on staying in Brazil like he was, it wasn’t helping anybody.”
Having agreed to move Costa out, Chelsea are set to be immediately reacquainted with him on Wednesday.
While the 28-year-old will play no part in the Champions League clash at Wanda Metropolitano, he is likely to be in attendance.
Lampard believes that encounter, followed by a crucial Premier League meeting with Manchester City, offers Conte’s side an opportunity to put down some serious markers regarding their claims to continental and domestic crowns.
He added: “Atletico is one of the hardest places to go in Europe, with the way they play and the atmosphere in the stadium.
“On Saturday, it does not get any easier with a home fixture against Manchester City.
“Pep Guardiola’s side are in great form, scoring a lot of goals and are three points clear of Chelsea in the Premier League table.
“If they win at Stamford Bridge, the gap will be extended to six, which is a fair amount all of a sudden.
“However, should Chelsea get through these two fixtures unscathed, then it will send out a real message of intent.”