Along with farm exports and tourism, the funds are a key source of foreign exchange and are tracked by traders.
"The cumulative inflows in 2021 were a record of $3,718 million ... a 20.2% increase," the bank said in its weekly bulletin on Friday.
The full year 2021 remittances were above a September central bank forecast of $3.4 billion.
The bank said December's remittances of $350.6 million were also an all-time monthly record.
(Reporting by George Obulutsa; editing by Jonathan Oatis)