  Mobile impurities in a Bose-Einstein condensate form quasiparticles called
polarons. Here, we show that two such polarons can bind to form a bound
bipolaron state. Its emergence is caused by an induced nonlocal interaction
mediated by density oscillations in the condensate, and we derive using field
theory an effective Schr\"odinger equation describing this for arbitrarily
strong impurity-boson interaction. We furthermore compare with Quantum Monte
Carlo simulations finding remarkable agreement, which underlines the predictive
power of the developed theory. It is found that bipolaron formation typically
requires strong impurity interactions beyond the validity of more commonly used
weak-coupling approaches that lead to local Yukawa-type interactions. We
predict that the bipolarons are observable in present experiments and describe
a procedure to probe their properties.
