Data was collected on hundreds of thousands of men from 15 European countries.
For British men, the average height at age 21 rose from 167.05cm (5ft 5in) in 1871-75 to 177.37cm (5ft 10in) in 1971-75.
A public health expert said height was a “useful barometer” but it was crucial to focus on improving health overall.
The paper, published in the journal Oxford Economic Papers, looked at data from sources including military records and modern population surveys from the 1870s to 1980 in 15 European countries.
It looked only at male height because there was too little historical data for women.
Genes may be commonly seen as the main determinant of height, but although they explain the difference between individuals, they would not explain the trend seen in this paper, its lead author said.
Prof Tim Hatton of the University of Essex said there was no “Darwinian explanation” to the trend. “People are surviving in the 20th Century who would not have survived in the 19th,” he added
The researchers said the gene pool “cannot account for substantial increases in mean stature over four or five generations”.