Researchers followed nearly 240,000 Swedish men for 35 years.
The analysis, published in the journal Gut, showed overweight teenagers went on to have twice the risk of bowel cancer. The figures were even higher in obese teens.
The World Cancer Research Fund said the link between obesity and cancer was "strong".
Bowel cancer is the third most common cancer in the world, with nearly 1.4 million new cases each year.
Processed red meat and abdominal fat have been linked to the disease.
The participants in the study were aged between 16 and 20 at the start.
The overwhelming majority were a normal weight, but 6.5% were overweight and 1% were obese.
There were 855 cases of colorectal cancer in the study.
However, the results showed not all weights were affected equally.
Those who were obese were 2.38 times more likely to have developed a bowel tumour.
The study, led by Orebro University Hospital in Sweden and Harvard University, said: "Late adolescence marks the transition from childhood to adulthood and is a period of accelerated growth, especially among men, thus this period may represent a critical window."
"It is important that we understand the role of exposures in childhood and adolescence in the development of colorectal cancer.
"In fact, the strong association observed between adolescent obesity and early-to-mid-life colorectal cancer, coupled with the increasing prevalence of adolescent obesity, may shed light on the increase in colorectal cancer incidence among young adults," he added.
Rachel Thompson, from the World Cancer Research Fund, said the evidence suggested that obesity was a risk factor for bowel cancer.
"This finding is interesting because it gives an indication that bowel cancer risk might be affected by our lifestyle habits throughout the life course," she said.
"In some ways, research into the relationship between factors like obesity and cancer risk is still in its infancy.
"It will be interesting to see if further research emerges in the future to back up the apparent relationship between body fatness in youth and later-life cancer risk."

30 May 2017 Last updated at 08:04 BST
Well, that's what happened to pupils at a London school when David Walliams turned up one morning.
The author and Britain's Got Talent judge surprised a hall of 200 children and gave some top tips for becoming a writer.
He also read extracts from his books, including Gangsta Granny and Windy Mindy from The World's Worst Children - the follow-up has just been released.
Watch the clip to see more.

The 25-year-old, who has helped Sarries to three Premiership titles, has played 152 times for the club since 2008.
Farrell has 52 caps for England and four for the British & Irish Lions.
"Owen has developed into one of the leading players in world rugby," Saracens director of rugby Mark McCall told the club website.
"He is one of our own, so for him to commit his long-term future to the club is huge news - we're delighted that he'll be extending his stay."
Farrell was named European player of the year in May, becoming the inaugural winner of the Anthony Foley Memorial Trophy.
He added: "It's an opportunity to hopefully grow with this group again for the next few years; to get better and improve on what we've already done."
Saracens begin their 2017-18 Premiership campaign at home to Northampton Saints on Saturday.
Being overweight in adolescence is linked to a greater risk of bowel cancer later in life, a study suggests.
[NEXT_CONCEPT]
Ever wanted a famous author to surprise your school assembly and give you writing tips?
[NEXT_CONCEPT]
England fly-half Owen Farrell has signed a new five-year contract with Saracens, keeping him with the European champions until 2022.