The deal values Talend at $2.4 billion, including net debt. Its shares at last check were 28% higher at $65.68.
The offer price reflects premiums of roughly 29% to Talend's closing price on Tuesday and 81% to the volume-weighted-average price over the past 12 months.
Thoma Bravo is the Chicago PE firm focused on software and technology-enabled services sectors.
"The last 12 months have underscored the importance of digital transformation" and Talend's role "in ensuring enterprises can trust the data fueling their business," Talend Chief Executive Christal Bemont said in a statement.
The agreement includes a 30-day go-shop period, expiring April 10, during which Talend's board and advisers may solicit alternative acquisition proposals.
Thoma Bravo plans a tender offer, which currently is expected to close in the third quarter. The redomiciling of Talend and related transactions are expected to close in the fourth quarter.
Talend, which went public in 2016, has about 1,400 employees and roughly 6,000 customers.
Last month, the company said that Sumitomo Life Insurance Co. had selected Talend Data Fabric for its data-analytics structure.
Thoma Bravo had about $77 billion in assets under management at Dec. 31. Since 2003 the firm has done 230 software deals valued at more than $68 billion.