Profits for the three months to March rose to $3.8bn (Â£2.6bn), compared with $2.1bn for the same period in 2015.
The stronger performance in Europe helped Ford to outpace Detroit rival General Motors.
Ford chief executive Mark Fields said the company had an "absolutely terrific start to the year".
Shares rose 3.2% in New York, but are still 11% lower than this time last year.
Ford's European business made a pretax profit of $434m in the quarter - higher than the total for all of last year - and substantially better than a $42m loss for the same period in 2015.
By comparison GM made a $6m loss in Europe during the first quarter of 2016, better than the $239m loss last year.
Ford remained the region's best-selling commercial vehicle brand, reflecting the popularity of the Transit and Ranger lineups.
In North America, Ford's F-150 trucks and SUVs were a major contributor to the company's profit growth.
Pretax profit in the region rose to $3.1bn, outpacing GM's $2.3bn and more than double the $1.5bn for the first quarter of 2015.
Earlier this month the company said it had set up a new subsidiary, Ford Smart Mobility, in a bid to combat growing competition from the technology sector.
Ford has been investing in driverless cars and earlier this year tested a self-driving vehicle in the snow.
Ford posted a record quarterly profit following strong sales in Europe and moving more pick-up trucks and SUVs in North America.