Konecny was born in London, Ontario and grew up in Clachan, a small community in the township of West Elgin. He played youth hockey for the Chatham-Kent Cyclones before moving to the Elgin-Middlesex Chiefs of the Minor Hockey Alliance of Ontario for his bantam and minor midget seasons. His minor midget coach Darren Kelly has said of him that, "When he was 10, we were in the Ontario finals in Oakville, and we were down 2–0 to the Toronto Marlies going into the third period ... Travis came out and scored four goals and an assist and we won 5–2. He was named the tournament MVP, and from that point on, his name was kind of on the radar." Konecny said at this point of his career that, "I feel I'm more of a playmaker and I try to win all my puck battles and races ... I find that an assist is just as good as a goal, and points don't matter to me as long as the team is winning."
The first scouting report from the team that would draft him into the OHL after his amateur career said of him: "Top-end forward with great hockey sense as well as skill. Moves the puck well at all times and competes in all situations." The assistant general manager that filed the report stated that over Konecny's time between that first report and his drafting he filed about 15 reports and stated of his consistency that "he never changed from first on my list 'til the day we drafted him". In his final season, Konecny had 53 goals and 61 assists in 54 games for the Elgin-Middlesex Chiefs.
Konecny was drafted first overall in the 2013 OHL Priority Selection by the 67's, winning the Jack Ferguson Award for first overall draft pick. After his first preseason training camp with the team he laughed that, "I took a few shots from the older guys, they were just letting me know I'm still a rookie ... I'm going to work hard and do whatever I can control and let things fall into place." He earned two primary assists in his first OHL game on September 20, 2013, and became a draw for fans in his first month with the team.
In October 2013 he was named the OHL Rookie of the Month, scoring four goals and five assists in eleven games over the month and remaining tied for OHL rookie scoring at the end of October. That month the Ottawa Citizen wrote that in terms of top professional prospects, "Travis Konecny seems to be the next one-to-watch." Konecny had a strong first year in the OHL, leading all rookies in points and goals. He was awarded the Emms Family Award for OHL rookie of the year as well as being named to the OHL's first rookie all-star team.
At the start of the 2014–15 OHL season, Konecny was named captain of the 67's. He finished the season with 68 points, good for second on the team in scoring. Konecny was drafted in the first round, 24th overall, by the Philadelphia Flyers in the 2015 NHL Entry Draft. On July 16, 2015, Konecny signed a three-year entry level contract with the team. In the following 2015–16 season, after producing 45 points in 29 games, Konecny was traded by the 67's in a blockbuster trade to the Sarnia Sting on January 7, 2016 for Sasha Chmelevski, Chase Campbell, and 10 draft picks, of which 2 are conditional.
On the afternoon of October 10, 2016, Philadelphia Flyers general manager Ron Hextall announced that Konecny had made the final roster effectively marking the beginning of Konecny's professional hockey career.
Konecny made his international debut playing for Canada at the 2014 IIHF World U18 Championships. He went on to play at the 2014 Ivan Hlinka Memorial Tournament, winning a gold medal. as the team captain. Konecny was selected to represent Canada at the 2016 IIHF World Junior Championships in Finland, tallying 2 points. In 2017 Konecny represented Canada at the World Championships.
Konecny is second cousins with Vancouver Canucks forward Bo Horvat.