Its Balfour Museum, which opened in 1994 has seen a fall in visitor numbers, said the charity.
Currently shut to visitors, the museum will officially close on December 31.Originally it was based the headquarters in Weeke before moving to Winnall in 2004.
Colin Brown, Red Cross operations director for the Hampshire, Isle of Wight and Surrey area, said that while much treasured by the organisation, the museum had not maintained a high public profile or visitor numbers.
Mr Brown said the decision was made prior to the decisions to move other services. However the knowledge that moving was likely sooner rather than later led to agreement with the Balfour Historic Museum Trust to close this year.
The museum displayed items from the Hampshire Red Cross branch, including archive material, photographs, and medals.
It was set up by long-running Hampshire branch director Elizabeth Balfour, who financed the museum from the beginning and continued to do so after her death in 1998 through the Balfour Historic Museum Trust.
The charity said the Portsmouth move was to better focus to go on the more heavily-populated Solent area. Refugee services, international humanitarian action and health and social care are moving to a premises on Commercial Road.
Emergency response services and medical equipment will be based in Eastleigh, at an as yet undisclosed location as negotiations are ongoing.
The Red Cross has signed a lease and some staff have already moved in with the rest of staff expected to complete the move in the New Year.
Although the Winnall site will be sold, Winchester will continue to have its own first aid group and medical equipment service in the area, the charity said.
Mr Brown said the measure had not been initiated as a cost-cutting exercise, but to make better use of the funds and resources the charity has and make it more community based.
“Where the big populations are we’re not as strong as we used to be or providing as much as we used to,” said Mr Brown.
He added that, rather than tying up money at the Winnall site, that money could now be released to deliver services.
Mr Brown added that a consultation was done with staff and volunteers to see how these changes would affect them and whether they would be able to move where needed, and said that he did not expect staff numbers to change.
He said the plans had been welcomed by the vast majority of staff and volunteers.