Tennessee sent the top selection along with its fourth- (No. 113) and sixth-round (No. 177) picks this year to the Rams in exchange for Los Angeles' first-round pick (No. 15), two second-round selections (Nos. 43 and 45) and a third-round pick (No. 76) in 2016. The Titans also will get the Rams' first- and third-round picks in 2017.
With the trade, the Rams now have the ability to draft the quarterback of their choice and make a splash as they settle into Los Angeles after leaving St. Louis this year. Carson Wentz of North Dakota State and Jared Goff of California are considered the top quarterback prospects.
A team source told ESPN's Adam Schefter that, as of Thursday, the Rams are leaning toward selecting Goff No. 1 overall but will use the time before they pick on April 28 to also consider Wentz.
"Our philosophy has always been to build through the draft," Rams general manager Les Snead said in a statement. "This trade is a reflection of that goal and [owner Stan] Kroenke's dedication to assembling a winning team on the field."
Sources told ESPN that the trade was agreed to Wednesday night but the Rams didn't want to steal any thunder from Kobe Bryant's final game. It was decided the Titans would announce the deal at 9 a.m. ET Thursday. Rams coach Jeff Fisher confirmed Thursday that the Rams asked Titans to keep the trade quiet until the next day.
"There was no need for the news of the trade to get out while Kobe was playing his last game," one Rams official told ESPN. "Kobe deserved his night, and there was no reason for this trade to be announced on his night."
The Titans now own nine selections in the 2016 draft, including six of the top 76 picks.
"It is not often that you have the No. 1 overall pick and we hope to not be in this position again. But we tried to use that pick as currency to work the draft and maximize player acquisition," Titans general manager Jon Robinson said in a release. "We now have the ammunition to work the draft and acquire players that are good for this football team.
"In terms of timing, it made sense for us to do this now as it gives us time to adjust and make sure we target more players."
Robinson said during a news conference Thursday that he wasn't actively shopping the No. 1 pick but listened to teams that reached out to him.
League sources told ESPN's Ed Werder that the Philadelphia Eagles -- despite signing Sam Bradford and Chase Daniel this offseason -- were among the teams expressing interest in the No. 1 pick but withdrew from discussions earlier this week.
Believing they had their franchise quarterback in 2010 No. 1 overall pick Bradford, the Rams traded away a high draft pick in 2012, sending the No. 2 overall selection to the Washington Redskins for three first-round picks and a second-rounder. Washington used that No. 2 pick to select Robert Griffin III.
Neither quarterback worked out for his team. Bradford was dealt to the Eagles in a March 2015 trade, and Griffin signed with the Cleveland Browns last month after being released following a 2015 season in which he did not take the field.
The Rams previously traded for the No. 1 overall pick in 1997 when they moved up in a deal with the New York Jets to select offensive tackle and future Hall of Famer Orlando Pace.
The 2016 NFL draft begins April 28.
ESPN staff writer Nick Wagoner and The Associated Press contributed to this report.