Sterling gained versus the euro and dollar as traders readied for Johnson -- a leading Leave campaigner in Britain's shock Brexit referendum three years ago -- to take the reins from outgoing premier Theresa May.
He will be appointed later Wednesday by Queen Elizabeth II at Buckingham Palace.
Sterling had already rallied Tuesday in reaction to Johnson's election as Conservative Party leader, with investors keen to see whether he pushes ahead with a no-deal divorce from the European Union at the end of October.
- Brexit scepticism 'priced in' -
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"The pound is beginning to stabilise, proving that a lot of the scepticism about Boris Johnson's Brexit policy was already built into the price," said City Index analyst Fiona Cincotta.
"Sterling is trading a touch higher this morning," she noted.
May resigned after failing to get parliamentary support for a Brexit deal she had struck with EU leaders.
Meanwhile, Europe's major stock markets mostly fell, with miners weighed down by sliding iron ore prices, dealers said.
Heading towards midday, London's FTSE 100 was sharply down by 0.9 percent.
In the eurozone, Paris CAC 40 fell 0.5 percent but Frankfurt's DAX 30 won 0.3 percent in value.
"The FTSE 100 is firmly in the red as mining stocks are weighing on the index," said CMC Markets analyst David Madden.
"A sell-off in iron ore prices in China has prompted a decline in major mining stocks like Rio Tinto, BHP Billiton, and Glencore.
"Brazil's Vale won approval to restart iron ore production, and that triggered the drop in iron ore prices."
- Bright US earnings -
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Most Asian markets enjoyed another day of gains, with support coming from more healthy earnings results and renewed hopes for a resolution of the China-US trade war.
The latest big-name firms to post positive results were Coca-Cola, toymaker Hasbro and Harley-Davidson, helping all three main indexes on Wall Street end with sharp gains overnight.
Adding to the upbeat mood were reports that US President Donald Trump's Trade Representative Robert Lighthizer will lead a delegation to China next week to resume trade talks.
The meeting would be the first head-to-head talks since negotiations were cut short in May by Trump's surprise decision to hit China with more tariffs for what he called Beijing's backsliding.
- Key figures around 1045 GMT -
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Pound/dollar: UP at $1.2463 from $1.2440 at 2050 GMT
Euro/pound: DOWN at 89.38 pence from 89.64 pence
Euro/dollar: DOWN at $1.1140 from $1.1152
Dollar/yen: DOWN at 108.06 yen from 108.23 yen
London - FTSE 100: DOWN 0.9 percent at 7,491.71 points
Paris - CAC 40: DOWN 0.5 percent at 5,591.18
Frankfurt - DAX 30: UP 0.3 percent at 12,523.58
EURO STOXX 50: DOWN 0.1 percent at 3,527.95
Tokyo - Nikkei 225: UP 0.4 percent at 21,709.57 (close)
Hong Kong - Hang Seng: UP 0.2 percent at 28,524.04 (close)
Shanghai - Composite: UP 0.8 percent at 2,923.28 (close)
New York - Dow: UP 0.7 percent at 27,349.19 (close)
Brent North Sea crude: UP 0.2 percent at $63.98 per barrel
West Texas Intermediate: UP 0.4 percent at $57.01