In Smith's debut campaign in charge, he led Warriors to the Scottish x Italian Shield and a top-four finish as well as guiding them into their first European final.
Smith, who joined Glasgow Warriors last summer on a two-year contract from the Italian Rugby Federation, also helped the Warriors go the whole BKT URC regular season unbeaten at Scotstoun.
Smith said: "This is season one for this group. This is not the end for us, this is just the start. It's a stepping stone."
The former South Africa international led Italy during 2020 and 2021.
This award was voted for by the URC's 16 head coaches and leaves only one prize still to be announced - the Players' Player of the Season.