Kaut, 18, had 16 points (nine goals, seven assists) in 38 games with Pardubice in his native Czech Republic's top league last season. He also had seven points (two goals, five assists) in seven games for the Czech Republic at the 2018 IIHF World Junior Championship.
RELATED: [Kaut overcomes heart issue to pursue NHL dream with Avalanche]
"Martin plays a complete, two-way game," general manager Joe Sakic said after Colorado selected Kaut at the draft. "He competes, he's strong on the puck. He's got a great shot and he's a pure goal scorer. We just like the upside and what he can bring to our club."
Kaut is the fourth player selected in the first round of the 2018 draft to sign, joining forward Andrei Svechnikov, the No. 2 pick by the Carolina Hurricanes; forward Jesperi Kotkaniemi, the No. 3 pick by the Montreal Canadiens; and defenseman Adam Boqvist, the No. 8 pick by the Chicago Blackhawks.