We reconstruct the star formation history of the Sco-Cen OB association using a novel high-resolution age map of the region. We develop an approach to produce robust ages for Sco-Cen's recently identified 37 stellar clusters using the \texttt{SigMA} algorithm. The Sco-Cen star formation timeline reveals four periods of enhanced star formation activity, or bursts, remarkably separated by about 5 Myr. Of these, the second burst, which occurred 15 million years ago, is by far the dominant, and most of Sco-Cen's stars and clusters were in place by the end of this burst. The formation of stars and clusters in Sco-Cen is correlated but not linearly, meaning that more stars were formed per cluster during the peak of star formation rate. Most of the clusters, which are large enough to have supernova precursors, were formed during the 15 Myr period. Star and cluster formation activity has been continuously declining since then. We have clear evidence that Sco-Cen formed from the inside out and contains 100-pc long correlated chains of contiguous clusters exhibiting well-defined age gradients, from massive older clusters to smaller young clusters. These observables suggest an important role for feedback in forming about half of Sco-Cen stars, although follow-up work is needed to quantify this statement. Finally, we confirm that the Upper-Sco age controversy discussed in the literature during the last decades is solved: the region toward Upper-Sco, a benchmark region for planet formation studies, contains not one but up to nine clusters spanning ages from 3 to 19 Myr.