"Using specialist equipment the teams succeeded in locating and identifying the plane and recovering Mr Sala's body".
In a statement tonight police said they "will continue to be supported by specially-trained family liaison officers".
Dorset Police said they would continue to support the coroner's investigation into the circumstances of the crash.
The pair went missing on 21 January after the plane they were travelling on from Nantes to Cardiff crashed 21 miles (34km) off the coast of Guernsey.
After search operations were suspended, a shipwreck hunter hired by Sala's family with funds donated by football stars such as Lionel Messi found the wreckage on Sunday.
"The weather forecast is poor for the foreseeable future and so the hard decision was taken to bring the overall operation to a close".
The AAIB suspended the search on Thursday due to the poor weather conditions, while the body of Ibbotson has yet to be found.
Remotely operated Vehicles (ROVs) were used in tough conditions to pull the body out of the water in a "dignified" way, the Air Accidents Investigation Branch (AAIB) said.
The plane had requested to descend before it lost contact with Jersey air traffic control.
An official search operation was called off on January 24 after Guernsey's harbour master David Barker said the chances of survival after such a long period were "extremely remote".
Sala was headed to Cardiff to make his debut in the English Premier League after departing the French soccer club FC Nantes.
He said discovery had been so quick because the team had been looking for a static object rather than in a dynamic environment searching for survivors.
Sala was flying to join up with Cardiff City in what was the most expensive signing in the Welsh club's history.
Cardiff posted the statement on their website under a picture of the player. Cardiff are said to be "surprised" with the timing of the demand so soon after the tragedy.