The 30-year-old, who spent the last two years playing for Hellas Verona, will finalise the move on July 1.
Pisano will put pen to paper on a two-year contract, and arrives at Ashton Gate to bolster the right-back position following Mark Little's release.
Head coach Lee Johnson said: "Eros brings with him a winning mentality, having just won promotion with Verona. He's a tough cookie and that's what we're after in that position; resilience and strength to go along with the good young players - Zak Vyner and Taylor Moore - already competing in that place.
"He's strong physically, 6ft 1in tall and will add goals to us as well. It's great to have a big full back. His style is aggressive but he's also very athletic. He's competent on the ball, using it well and gets up and down the right side."
Pisano has spent his entire career so far playing in Italy, representing Varese, Pisa, Palermo, Genoa and Verona.