We report the use of photoassociative spectroscopy to determine the ground-state s-wave scattering lengths for the main bosonic isotopes of strontium, 86Sr and 88Sr. Photoassociative transitions are driven with a laser red detuned by up to 1400 GHz from the 1S0-1P1 atomic resonance at 461 nm. A minimum in the transition amplitude for 86Sr at -494 +/- 5 GHz allows us to determine the scattering lengths 610a0 < a86 < 2300a0 for 86Sr and a much smaller value of -1a0 < a88 < 13a0 for 88Sr.