The 5-foot-7 point guard, who averaged 16.5 points and over 5 assists per game in leading UConn to an undefeated season, was the fourth player picked in the WNBA draft.
There was talk that Montgomery could be the draft's top pick, but instead she became the second point guard chosen, behind Maryland's Kristi Toliver, who went to Chicago with the third pick.
"I know that teams have to get exactly what they need this year, and it's never a disappointment when you're drafted," Montgomery said.
Louisville's Angel McCoughtry went to Atlanta with the top pick, and Marissa Coleman of Maryland was chosen second by Washington.
The Lynx, who went 16-18 last year, had three of the first 15 picks in the draft. They chose center Quanitra Hollingsworth from VCU with the ninth pick and forward Rashanda McCants of North Carolina with the 15th pick.
Montgomery also joins former Stanford star Candice Wiggins and former LSU standout Seimone Augustus on the Lynx. She becomes the second UConn player chosen by Minnesota in two years. Charde Houston was their third-round pick a year ago.
"It's always good when you go somewhere new to just know somebody in that area that can show you around," Montgomery said. "I'm excited. I'm anxious again to go to a new place, and relief that, yes, I do know where I'm going."
UConn coach Geno Auriemma called it a storybook ending to Montgomery's college career, but said it will take time for her to become a WNBA star.
"That's not an easy position to play when you come out of college," he said. "It's like coming out of college and being a rookie quarterback. It's just not an easy position to play, but if you're tough enough and you work hard enough, you certainly become a great one and she certainly is going to become a great one."
Montgomery is the 20th UConn player drafted into the WNBA, and is the 13th former Husky currently in the league. She also is the 10th first-round pick in UConn history.
The Connecticut Sun chose center Chante Black from Duke with the 10th pick in the draft.
Black averaged over 14 points and over 8 rebounds and blocked 66 shots during her senior season.
Point guard Lindsay Whalen said Black could be a key piece for the Sun, who went 21-13 last season before losing in the first round of the playoffs to New York.
"She's a huge inside presence," said Whalen. "Obviously we have really talented front-line players, but 6-5 and long and athletic, so it's going to be really cool."
Black said Sun coach Mike Thibault has already told her he wants to see her throwing some elbows.
"He wants a rebounder," she said. "That's one key thing he keeps putting in my ear is rebounding."
The Sun also picked Lyndra Littles of Virginia with the 17th pick. She averaged 20 points a game for the Cavaliers, despite missing the first nine games of the season because she was academically ineligible.
Littles said she is comfortable playing on the wing or in the post.
"I can throw a few elbows," she said.
The Sun chose Alba Torrens, a member of the Spanish national team, with their third-round pick.
"The good thing for these kids coming in is they don't need to be stars for our team right away," said Thibault. "We have veterans. We grew up a lot last year. But we do need somebody to come in and play some minutes."
It will be tough for many draft choices to make a team this season.
The Houston Comets folded in the offseason and rosters league-wide have been slashed from 13 to 11 players, leaving 39 fewer jobs.