"This is a guy we believe in," McVay said. "We're encouraged and excited about developing him."
Goff, the first-overall pick in the 2016 NFL Draft out of the University of California, Berkeley, had a rough rookie season.
After failing to win the first-string job in camp, he took a beating in seven starts as he was sacked 26 times. The Rams also failed to win a game with Goff as the starter.
"Coming out of my meeting, I felt like it was a guy that I would love to play for, and hopefully play a long time for," Goff said. "I expect him to bring out the best in me."
McVay, who at 30 years old became the youngest head coach in NFL history, will call plays for the Rams' offense.
The team's offense has ranked as the worst in the NFL for two straight seasons.
"It's going to be a challenge, and it won't be easy," McVay said. "But I can't wait to go to work."
McVay was offensive coordinator for the Washington Redskins under head coach Jay Gruden. In 2016, Washington finished third in the NFL in total yards and second in total passing yards.
In comparison, Washington ranked No. 25 in total offense in 2013, the year before McVay took over the offense.
McVay is also known for his work developing quarterback Kirk Cousin, who twice broke Washington's records for yards passing and completions under McVay. The Rams'front office hopes McVay can produce similar results with their 22-year-old quarterback.
"We are a young offense and having a guy like that who can relate to us a little better could be beneficial, but at the same time I think his overall knowledge and leadership and coaching skills are far more important," Goff said.
Goff says McVay's coaching skill outweighs his young age. Excited to have a young coach as a young quarterback.— Ashley Brewer (@abc7ashley) January 13, 2017
McVay's coaching staff began to take shape as he confirmed 69-year-old NFL veteran Wade Phillips would be his defensive coordinator and that the Rams would be retaining longtime special teams coordinator John Fassel.
Fassel served as interim coach of the Rams for the last three games after Jeff Fisher was fired as head coach following a 4-9 start in 2016.
Fisher, who was hired in 2012, amassed a record of 31-45-1 with the team.
McVay, who is younger than one Rams player, defense lineman William Hayes, said he valued the faith the Rams' front office has placed in him.
"It means everything. It makes you want to do a great job for the people who have shown that belief in you and that you can handle this role," McVay said. "It makes you feel a sense of accountability to Kevin Demoff, Les Snead and Stan Kroenke for being able to show that faith and I feel a big responsibility to making them right on that decision."
The Associated Press contributed to this report.