[5] Murphy graduated from Bolles School in Jacksonville, Florida in 2013 and attended the University of California, Berkeley.

Swimming for the California Golden Bears (Cal), he was an eight-time NCAA individual national champion, winning the 100-yard and 200-yard backstrokes in 2014, 2015, 2016, and 2017.

At the 2011 World Junior Swimming Championships in Lima, Murphy won a bronze medal in the 200-meter backstroke with a time of 1:59.63.

Murphy earned a gold medal in the 4×100-meter medley relay for his participation in the heats, swimming the backstroke leg with a time of 50.91.

He also placed third in the 200-yard IM in 1:40.27 and was once again was named CSCAA Swimmer of the Meet, this time sharing the title with former Bolles teammates Joseph Schooling and Caeleb Dressel.

[15][16] At the 2016 Summer Olympics in Rio de Janeiro, Murphy won gold medals in the 100- and 200-meter backstroke, as well as in the 4×100-meter medley relay together with Cody Miller, Michael Phelps, and Nathan Adrian.

[20][21] It also marked the sixth consecutive time a swimmer representing the United States had won the gold medal in the 100-meter backstroke at the Olympic Games.

[20] His gold medal was also the first won by a male alumnus of a high school in Jacksonville, Florida for the United States in an individual swimming event.

[3][17][19] At the 2017 NCAA championships, Murphy completed his four-for-four sweep of the 100- and 200-yard backstroke events, becoming only the fourth man in NCAA history to sweep 100- and 200-yard events of a single stroke four years in a row after John Nabor (backstroke), Pablo Morales (butterfly), and Brendan Hansen (breaststroke).

[1] Murphy's strong finish to the Championships, winning two gold medals on the final day of competition, was noted by Jacksonville newspaper The Florida Times-Union.

[25] His gold medal performance in the 200-meter backstroke with a time of 1:53.57 established a new Championships record that was over 1.5 seconds faster than the silver medalist in the event, Ryosuke Irie.

[30] In July 2019 at the 2019 World Aquatics Championships in Gwangju, South Korea, Murphy won three medals.

Swimming with Lilly King, Caeleb Dressel, and Simone Manuel in the final of the mixed 4×100-meter medley relay, he won a silver medal.

[38] He swam a time of 1:54.20 in the final, winning the event and securing a spot at the 2020 Summer Olympics in the 200-meter backstroke.

[42][43] On day two of Olympic competition, in the prelims of the 100-meter backstroke, Murphy swam a 53.22 and tied in overall ranking for seventh with Russian Evgeny Rylov.

Murphy held off the field in his leg of the relay, tying Thomas Ceccon of Italy for first at the wall.

[59][60] Additionally, Murphy's support of his teammates and the integrity of swimming as a sport, as well as his consistent performances since the 2016 Summer Olympics, earned him a nomination for the Male Athlete of the Year Golden Goggle Award.

[69] Starting off his third and final playoffs match of the season, Murphy won 19.0 points for his team in one race, winning the 200-meter backstroke in a personal season-best time of 1:48.10.

[83] 2024 Murphy placed first in the US Olympic Trials in the 200 M backstroke, becoming the first swimmer to win both the 200 and 100 events three years in a row.

[85] As of June 21, 2024[update] Legend: r – relay lead-off leg a with Michael Andrew (breaststroke), Caeleb Dressel (butterfly), Zach Apple (freestyle) Legend: WR – World record; r – relay lead-off leg a split 51.85 in backstroke; with Cody Miller (breaststroke), Michael Phelps (butterfly), Nathan Adrian (freestyle) b split 52.31 in backstroke; with Michael Andrew (breaststroke), Caeleb Dressel (butterfly), Zach Apple (freestyle) Murphy began dating Bridget Konttinen who he met in college, in 2016.

[99] Murphy was raised in a strong Catholic family and remains committed to his faith, stating, "I’m a firm believer in God.