The discrepancy between observations from γ-ray astronomy of the ^{60}Fe/^{26}Al γ-ray flux ratio and recent calculations is an unresolved puzzle in nuclear astrophysics. The stellar β-decay rate of ^{59}Fe is one of the major nuclear uncertainties impeding us from a precise prediction. The important Gamow-Teller strengths from the low-lying states in ^{59}Fe to the ^{59}Co ground state are measured for the first time using the exclusive measurement of the ^{59}Co(t,^{3}He+γ)^{59}Fe charge-exchange reaction. The new stellar decay rate of ^{59}Fe is a factor of 3.5±1.1 larger than the currently adopted rate at T=1.2 GK. Stellar evolution calculations show that the ^{60}Fe production yield of an 18 solar mass star is decreased significantly by 40% when using the new rate. Our result eliminates one of the major nuclear uncertainties in the predicted yield of ^{60}Fe and alleviates the existing discrepancy of the ^{60}Fe/^{26}Al ratio.