The Bills and Lions also came up as potential options for Webster.
Webster worked out for the Texans earlier in the day it looks like everything went well enough for the parties to hammer out a deal.
Webster, 27, is a former third-round pick of the Broncos back in 2013. He has played out his four- year, $2,745,800 contract before signing a two-year, $7.75 million contract that included $4.25 million guaranteed with the Rams last March.
Webster was set to make a base salary of $3 million for the 2018 season when the Rams released him in a move that cleared $3,546,875 million of available cap space.
In 2017, Webster appeared in 11 games and recorded 38 tackles, one interception and seven pass defenses.
We had him featured in our Top 50 Available 2018 NFL Free Agents list.