The couple divorced in June after nearly five years of marriage. They split up in the wake of media reports that James had cheated on Bullock with numerous women throughout their relationship.
"I support Jesse in his move to Austin," Bullock told People magazine. "We have both moved on with our lives and only want the best for each other. Anything else that is said on my behalf is inaccurate."
Bullock finalized her adoption of an 8-month-old son named Louis last week, while James was recently seen out and about with "LA Ink" star Kat Von D.