It appears the F-35 will have a combat radius greater than the F-16 (the aircraft it will replace in the largest numbers) greater than the Sea Harrier and Harrier, and similar to the F-18 series.
Not the F-35B, which has a similar fuel fraction to most current supersonic fighters but can't, at present, carry external fuel. It has a claimed 450 nm high-medium-medium-high radius of action with about 3000 lb of weapons; the AV-8B (says the manual) can manage 460 nm on a high-lo-high with 6 x Mk82s and two 300 gal tanks.
3694 AV-8B Harrier II Standard Aircraft Characteristics - October 1986