The European Union named Paolo Gentiloni its new economic-affairs commissioner, charged with navigating the bloc through tax policy issues, including taxing of global tech giants.

Gentiloni, a Socialist former Italian prime minister, is due to take over from France’s Pierre Moscovici and will also enforce the bloc’s limits on national budget deficits and debt loads.

The position is politically sensitive as the EU seeks both to contain euroskeptic forces such as Italy’s own Matteo Salvini who are intent on challenging Europe’s fiscal rule book and to offer room for growth-boosting domestic spending.

Gentiloni emerged as Italy’s appointee to the next...