The banks reached a final merger agreement late last year to create a lender with total assets of 80 billion riyals (17 billion pounds).
The combined lender will be rebranded as Lusail Bank, the sources said, adding the integration would begin towards the end of the first quarter.
Barwa Bank did not respond to a request for immediate comment.
A shake-up has been long mooted in Qatar's banking system, where 18 local and international commercial banks serve a population of around 2.6 million.
Barwa Bank said last month its shareholders had approved the proposed merger.
Two of the United Arab Emirates' biggest banks linked up to create First Abu Dhabi Bank in 2017.
Since then, two major bank mergers have been announced in Saudi Arabia, Kuwait Finance House is buying Bahrain's Ahli United, and Abu Dhabi Commercial Bank is leading a three-way merger in the United Arab Emirates.
"Slow growth and subdued credit demand in the region is one of the biggest drivers of consolidation," Ashraf Madani, a senior analyst at Moody's said in a recent report.
"This has intensified competition for depositors and borrowers, dampening profits at GCC (Gulf Cooperation Council) banks."
Credit Suisse advised Barwa on the transaction while IQB was advised by Perella Weinberg.
(Additional reporting by Davide Barbuscia; editing by Jason Neely)
By Hadeel Al Sayegh