On 7 February 2019, Valančiūnas was traded, along with C. J. Miles, Delon Wright and a 2024 second-round draft pick, to the Memphis Grizzlies in exchange for Marc Gasol. On 12 February, after being medically cleared to return from the thumb injury, Valančiūnas made his debut for the Grizzlies, recording 23 points and 10 rebounds in a 108–107 loss to the San Antonio Spurs. On 20 March, Valančiūnas scored a then career-high 33 points and had 15 rebounds in the Grizzlies' 126–125 overtime win over the Houston Rockets. Two days later, he had 23 points and career-high 24 rebounds in a 123–119 overtime loss to the Orlando Magic. He set the franchise record for defensive rebounds in a game (23), surpassing Shareef Abdur-Rahim, who had 18 defensive boards twice. On 30 March, he set a new career high with 34 points to go with 20 rebounds (11 offensive) in a 120–115 win over the Phoenix Suns. It was a career-best sixth straight double-double for Valančiūnas, with the streak ending the next day against the Los Angeles Clippers after injuring his right ankle in the third quarter. On 1 April, he was ruled out for the rest of the season with a grade II right ankle sprain.
On 11 July 2019, Valančiūnas signed a reported three-year, $45 million contract with the Grizzlies. On 28 February 2020, Valančiūnas improved his career record by grabbing 25 rebounds (6 offensive), however his team lost 101–104 to the Sacramento Kings. On 29 February 2020, he scored 22 points, grabbed 20 rebounds and improved the Grizzlies club record (45 rebounds) for the most rebounds in two consecutive games (previously the record belonged to Zach Randolph who had 42 rebounds in 2009), helping his team to crush the Western Conference leaders Los Angeles Lakers 105–88. On 13 August 2020, Valančiūnas achieved his career's first triple-double: 26 points (including 2/3 three-pointers), 19 rebounds, 12 assists and led his team to a crucial victory, which secured chances to play in the 2020 NBA playoffs, versus the Eastern Conference leaders Milwaukee Bucks.
In 2019, Valančiūnas represented the national team at the 2019 FIBA Basketball World Cup where Lithuania finished 9th overall. Valančiūnas led his team in total points and rebounds, averaging 14.0 points and 8.8 rebounds.