The game at Cardiff City Stadium went into penalties after neither team managed to score after 90 minutes of normal time and 30 minutes of extra time.
Poland goalkeeper Wojciech Szczęsny, who saved a penalty from Wales' Daniel James, was named the man of the match, news outlets reported.
Poland last Thursday beat Estonia 5-1 in a playoff semifinal and needed to defeat Wales in a final playoff on Tuesday night to earn a berth at the continental tournament in Germany.
A total of 12 teams were vying for the three remaining Euro 2024 spots in two-stage, single-leg playoffs this month.
The winners of the three playoff paths will complete the 24-team Euro 2024 lineup, joining 20 teams that advanced from the 10 qualifying groups plus hosts Germany, European football's governing body UEFA has said.
Poland missed out on a chance to qualify directly for Euro 2024, after drawing 1-1 with the Czech Republic in their last qualifying game in Warsaw in November.
Poland won 11 points from eight matches in their qualifying Group E, which also included Albania, Moldova and the Faroe Islands.
The Euro 2024 tournament will be held from June 14 to July 14 in 10 cities in Germany, with the final played at Berlin's Olympiastadion.
The Poles will face France, the Netherlands and Austria in the group stage of the tournament, following a draw in Germany in December.
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Source: IAR, PAP
Click on the audio player above for a report by Radio Poland's Marcin Matuszewski.