The journals were written by sailors on board HMS Trincomalee, which is berthed in Hartlepool.
The vessel, built in 1817, is being incorporated into the new National Museum of the Royal Navy (NMRN).
The journals have been sitting in Royal Navy archives in Portsmouth for the past 150 years.
Built in India in 1817, HMS Trincomalee was brought to Hartlepool in 1987, where it took more than 10 years to restore. It is now the main attraction at Hartlepool's Maritime Experience and attracts 54,000 visitors a year.
Bryn Hughes, general manager of the HMS Trincomalee Trust said: "The positive links with the NMRN in Portsmouth will heighten public awareness of HMS Trincomalee.
"It is a wonderful long-term scheme following hard on the profile of the recent Tall Ships Races so successfully staged in Hartlepool."
The rarely seen journals will eventually be included in the static Trincomalee exhibition in Hartlepool.
One journal dates from 1852 and was kept by midshipman William Dawson. It contains a detailed log and tracking maps of the journeys that HMS Trincomalee took during that period.
Dr Dominic Tweddle, director general of the NMRN, said: "The opportunity to welcome HMS Trincomalee as a part of the museum means that the story of the Royal Navy, its ships and its people can now be told on a national scale."
HMS Trincomalee was built for the Admiralty in Bombay and served in the West Indies and the Pacific.
It was stationed in West Hartlepool between 1862 and 1877 as a training ship.
Crew diaries which had been locked away for 150 years are being reunited with Britain's oldest surviving warship at a special ceremony on Teesside.