RAF Scampton, which was also home to 617 Squadron as they prepared for the Dambusters mission in World War Two, has housed the Red Arrows since 2000.
Six hundred people currently work at the site near Lincoln.
The MoD, which wants to save £3bn by 2040, is also closing RAF Linton-on-Ouse in North Yorkshire where 300 people work.
The government said RAF Scampton will close in 2022 with the Red Arrows relocating to a site "more fit for purpose".
Plans were also confirmed to transfer basic and fast jet training from RAF Linton-on-Ouse in North Yorkshire to RAF Valley on Anglesey in 2019 and cease using Linton in 2020.L