He is overwhelmed at how Rockets general manager Daryl Morey described him as having a chance "to be a great player and really be special in this league."
Williams was acquired by Houston from the New Jersey Nets in a three-team trade that also involved the Los Angeles Lakers.
"It means a lot," Williams said. "The fact that a team like the Rockets makes you feel wanted makes you comfortable and gives you confidence so that you can go out there and do your job."
The Nets took Williams with the 11th pick of the 2009 NBA Draft out of Louisville.
Terrence Williams Joins Rockets
"I feel like they got a steal," Williams said referring to the fact the Rockets gave up a lottery-protected 2012 first-round pick. "Not to be cocky and arrogant, but I don't feel I've been able to prove myself in this league yet.
"With the minutes I've gotten I've not been able to show what I can do."
In ten games this season Williams averaged 6.7 points.
Williams is equally pleased with the fact that the issues he had with the Nets haven't affected the Rockets' judgement.
Williams had been punished by the Nets for being late to meetings and practices.
Terrence Williams Joins Rockets
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