It was popular in several European countries, becoming a top-five hit on the German, Austrian and Swiss charts (reaching number one on the latter).

I had a four-channel, reel-to-reel tape deck, so I recorded the mandolin part, then added guitar, bass and a vocal, which was enough to make it sound like a little group.

"[4] Allmusic reviewer Mike DeGagne praised both "Boat on the River" and fellow Cornerstone single "Lights" for their "silky harmonies and welcoming choruses".

[5] Canadian Press critic Michael Lawson said it has a "Russian folksong flavor" and called it a "showcase for Shaw's balalaika-like mandolin work"[6] The Pittsburgh Press critic Pete Bishop called it a "zippy Mediterranean-style dance on which Tommy Shaw stars on mandolin" and "a fine novelty number.

The 1994 Slovenian song "Mlinar na Muri", which immediately became hit and eventually evergreen, with new lyrics by Tomaž Domicelj, sampled the melody of this tune.