We investigate the age constraints that can be placed on the double pulsar system using models for the spin-down of the first-born 22.7-ms pulsar A and the 2.77-s pulsar B with characteristic ages of 210 and 50 Myr respectively. Standard models assuming dipolar spin-down of both pulsars suggest that the time since the formation of B is ~50 Myr, i.e. close to Bs characteristic age. However, adopting models which account for the impact of As relativistic wind on Bs spin-down we find that the formation of B took place either 80 or 180 Myr ago, depending the interaction mechanism. Formation 80 Myr ago, closer to Bs characteristic age, would result in the contribution from J0737-3039 to the inferred coalescence rates for double neutron star binaries increasing by 40%. The 180 Myr age is closer to As characteristic age and would be consistent with the most recent estimates of the coalescence rate. The new age constraints do not significantly impact recent estimates of the kick velocity, tilt angle between pre and post-supernova orbital planes or pre-supernova mass of Bs progenitor.
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