We use the age-metallicity distribution of 96 Galactic globular clusters (GCs) to infer the formation and assembly history of the Milky Way (MW), culminating in the reconstruction of its merger tree. Based on a quantitative comparison of the Galactic GC population to the 25 cosmological zoom-in simulations of MW-mass galaxies in the E-MOSAICS project, which self-consistently model the formation and evolution of GC populations in a cosmological context, we find that the MW assembled quickly for its mass, reaching ${25,50}%$ of its present-day halo mass already at $z={3,1.5}$ and half of its present-day stellar mass at $z=1.2$. We reconstruct the MWs merger tree from its GC age-metallicity distribution, inferring the number of mergers as a function of mass ratio and redshift. These statistics place the MWs assembly $textit{rate}$ among the 72th-94th percentile of the E-MOSAICS galaxies, whereas its $textit{integrated}$ properties (e.g. number of mergers, halo concentration) match the median of the simulations. We conclude that the MW has experienced no major mergers (mass ratios $>$1:4) since $zsim4$, sharpening previous limits of $zsim2$. We identify three massive satellite progenitors and constrain their mass growth and enrichment histories. Two are proposed to correspond to Sagittarius (few $10^8~{rm M}_odot$) and the GCs formerly associated with Canis Major ($sim10^9~{rm M}_odot$). The third satellite has no known associated relic and was likely accreted between $z=0.6$-$1.3$. We name this enigmatic galaxy $textit{Kraken}$ and propose that it is the most massive satellite ($M_*sim2times10^9~{rm M}_odot$) ever accreted by the MW. We predict that $sim40%$ of the Galactic GCs formed ex-situ (in galaxies with masses $M_*=2times10^7$-$2times10^9~{rm M}_odot$), with $6pm1$ being former nuclear clusters.
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