This paper uses statistical and $N$-body methods to explore a new mechanism to form binary stars with extremely large separations ($> 0.1,{rm pc}$), whose origin is poorly understood. Here, ultra-wide binaries arise via chance entrapment of unrelated stars in tidal streams of disrupting clusters. It is shown that (i) the formation of ultra-wide binaries is not limited to the lifetime of a cluster, but continues after the progenitor is fully disrupted, (ii) the formation rate is proportional to the local phase-space density of the tidal tails, (iii) the semimajor axis distribution scales as $p(a)d asim a^{1/2}d a$ at $all D$, where $D$ is the mean interstellar distance, and (vi) the eccentricity distribution is close to thermal, $p(e)d e= 2 e d e$. Owing to their low binding energies, ultra-wide binaries can be disrupted by both the smooth tidal field and passing substructures. The time-scale on which tidal fluctuations dominate over the mean field is inversely proportional to the local density of clumps. Monte-Carlo experiments show that binaries subject to tidal evaporation follow $p(a)d asim a^{-1}d a$ at $agtrsim a_{rm peak}$, known as Opiks law, with a peak semi-major axis that contracts with time as $a_{rm peak}sim t^{-3/4}$. In contrast, a smooth Galactic potential introduces a sharp truncation at the tidal radius, $p(a)sim 0$ at $agtrsim r_t$. The scaling relations of young clusters suggest that most ultra-wide binaries arise from the disruption of low-mass systems. Streams of globular clusters may be the birthplace of hundreds of ultra-wide binaries, making them ideal laboratories to probe clumpiness in the Galactic halo.
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