  The breakout reaction $^{15}$O($\alpha,\gamma$)$^{19}$Ne, which regulates the
flow between the hot CNO cycle and the rp-process, is critical for the
explanation of the burst amplitude and periodicity of X-ray bursters. We report
on the first successful measurement of the critical $\alpha$-decay branching
ratios of relevant states in $^{19}$Ne populated via
$^{19}$F($^3$He,t)$^{19}$Ne. Based on the experimental results and our previous
lifetime measurements of these states, we derive the first experimental rate of
$^{15}$O($\alpha,\gamma$)$^{19}$Ne. The impact of our experimental results on
the burst pattern and periodicity for a range of accretion rates is analyzed.
