InContact said the sale would be worth $940 million, or $14 a share, in cash, representing a 55 percent premium from its closing price on Tuesday.
"We strongly believe that this transaction best positions the Company to execute on our vision of helping our customers deliver exceptional customer experiences, while rewarding our existing stockholders for the work we have achieved to date," inContact CEO Paul Jarman said in a statement.
"We worked hard to make this deal happen because we understand the tremendous value that inContact can bring to its customers and the marketplace," Nice CEO Barak Eilam said in a statement.
The transaction is expected to close in the second half of this year.
InContact's stock was down about 5.5 percent in 2016. It closed on Tuesday at around $9. By midmorning Wednesday, it jumped to $13.87.
inContact in 2016
Nice's stock was up 3 percent, near $65.90.
— Reuters contributed to this report.