"My assistant Walter's reaction when he found out I was buying him a house for Christmas!" Hudson wrote in the caption for a video clip she posted on Instagram this week.
Williams can be seen in the video dropping the paperwork for the house on the ground, then screaming, "What?" before giving Hudson a huge bear hug.
The video did not indicate where the house is located.
E! News said Hudson and Williams have been friends since they were students at Yale Elementary in Chicago.
"Walter and I have been friends since sixth grade," Hudson told The Advocate magazine in 2011. "He's by far my closest friend."