Verstraete obtained a degree of electrical engineering in Louvain and of Master in Physics from Ghent University, and obtained his PhD on the topic of quantum entanglement in 2002 under supervision of Bart De Moor and Henri Verschelde at the KU Leuven.

After working as a postdoc at the Max Planck Institute for Quantum Optics in the group of Ignacio Cirac (2002–2004) and at the California Institute of Technology (2004–2006), he became full professor and the chair of theoretical quantum nanophysics at the University of Vienna in 2006.

He moved back to Ghent University with an Odysseus grant from the FWO in 2012, where he has since built a large research group on applications of entanglement in quantum many-body systems.

Among his notable contributions is the discovery that there are nine different ways (represented by equivalence classes under stochastic LOCC operations (SLOCC)) in which four qubits can be entangled,[3] the theoretical demonstration that a universal quantum computer can be realized entirely by dissipation,[4] and the development of a quantum generalization of the classical Metropolis algorithm to find ground states of many-body Hamiltonians.

Among others, he was among the authors introducing fermionic PEPS, continuous MPS, and matrix product operators, and he is co-author of a highly cited review on the topic.