A method of connecting to an existing wellbore downhole can include installing a swellable material into the existing wellbore from a connecting wellbore drilled into the existing wellbore. A well system can include a relief wellbore drilled proximate an existing wellbore, a connecting wellbore drilled from the relief wellbore to the existing wellbore, a tubular string extending from the relief wellbore through the connecting wellbore and into the existing wellbore, and a swellable material which swells in an annulus formed between the tubular string and at least one of the relief wellbore, the connecting wellbore and the existing wellbore. Another method of connecting to an existing wellbore downhole can include drilling a relief wellbore proximate the existing wellbore, then drilling a connecting wellbore from the relief wellbore to the existing wellbore, and then installing a swellable material into the existing wellbore from the connecting wellbore.