Trades can't become official until the new NFL league year opens on March 14.
Los Angeles gets the Giants' fourth-round and sixth-round picks in the 2018 draft.
The Giants also obtained the Rams' 2019 seventh-round pick in the deal.
Ogletree will fill the Giants' need for quality veteran linebackers as they rebuild from their 3-13 season, arguably the worst in franchise history.
On the Rams' end, the trade is somewhat surprising, and that's because they just signed Ogletree to a four-year, $42 million extension in October.
Ogletree, 26, had 95 tackles, 2.0 sacks, one interception and one forced fumble last season in 15 games, all as a starter.
Despite their overall success last season under coach Sean McVay, the Rams clearly are reconfiguring their defense in Phillips' preferred image while clearing salary cap space.
The Chiefs could have probably afforded that but it would've made it hard to sign other players in the coming years.