Monday will be the first day in power for 109 new Conservative lawmakers who won seats in Thursday's election.
Over the weekend, Conservative politicians repeated their pledge to bring the UK out of the European Union by Jan. 31 and reach a new trade deal with the EU by the end of 2020.
Johnson intends to re-submit the Withdrawal Agreement Bill to parliament for ratification before Christmas.
The pound rose by as much as 0.7pc versus a slightly weaker dollar in early London trading, last up 0.4pc at $1.3379 .
Versus the euro, it was up around 0.15pc at 83.235 pence.
"Generally, market participants are still relatively optimistic over the outlook for the pound following the strong Tory majority - that's still encouraging demand for the pound even at these higher levels," said MUFG currency analyst Lee Hardman.
London's blue-chip share index, the FTSE 100, was up for the fourth session in a row.
The index usually moves in the opposite direction to sterling, because its constituent companies are export-focussed, so the synchrony indicates that the potential for Brexit clarity is benefiting both domestic and internationally focussed companies.
According to weekly futures data, speculators reduced their net short position to $1.861 billion in the week to Dec. 10, the lowest level of shorts since May.
UK manufacturing and services PMI data for December are due at 9.30 GMT. Reuters polling shows analysts expect a decline.
MUFG's Hardman said expectations for UK PMIs had been softened by weak eurozone PMIs earlier on Monday morning.
The Bank of England meets on Thursday.
"The likeliness of a hawkish tilt in the message appears quite small, so the upside potential for sterling seems broadly limited in coming days unless we start to see some details on the WA (Withdrawal Agreement)," analysts at ING wrote in a note to clients.