In the final season of a three-year, entry-level contract he signed March 30, 2021, Boldy signed a seven-year, $49 million contract with the Minnesota Wild on Jan. 16, 2023, an average annual value of $7 million.

Boldy was chosen by the Wild with the No. 12 pick in the 2019 NHL Draft. He was named a top 10 finalist for the 2021 Hobey Baker Award, given to the best NCAA Division I player in men's ice hockey as a sophomore for Boston College after he had 31 points (11 goals, 20 assists) in 22 games. He signed a three-year, entry-level contract with the Wild on March 31, 2021, and played for Iowa in the American Hockey League for the remainder of that season.

Boldy had 28 points (10 goals, 18 assists) in 24 games over two AHL seasons after he broke his left ankle during a preseason game against the Chicago Blackhawks on Oct. 7, 2021. He had 10 points (four goals, six assists) in 10 AHL games before scoring in his NHL debut a few miles from home in a 3-2 victory at the Boston Bruins on Jan. 6, 2022. Boldy had his first NHL hat trick in a 7-4 win against the Detroit Red Wings on Feb. 14, becoming the fourth rookie in Wild history to score three goals in one game, joining Justin Fontaine (Jan. 9, 2014), Kirill Kaprizov (March 12, 2021) and Rem Pitlick (Nov. 13, 2021).

Boldy played for the runner-up United States at the 4 Nations Face-Off and won gold with Team USA at the Olympic Winter Games Milano Cortina 2026, the country's first in men's Olympic hockey since the 1980 Lake Placid Games. He scored six minutes into the United States' 2-1 overtime win against Team Canada, the fastest by any team to start a gold medal game in an Olympic Games with NHL players, ahead of Team USA's Tony Amonte (8:49 at the 2002 Salt Lake City Olympics).

Shortly after returning home, Boldy was named the NHL Third Star for the week ending March 1 after a League-high seven points (three goals, four assists) in three games during that stretch.

A native of Millis, Massachusetts, Boldy earned a tryout for the USA Hockey National Team Development Program. He made the team and led the NTDP with 11 goals as a rookie in 2017-18 and received an A rating on NHL Central Scouting's preliminary players to watch list in his first year of NHL Draft eligibility.