The study, by the Institute of Education, London University, examined the reading habits of 6,000 children.
It indicated reading for pleasure was more important to a child's development than how educated their parents were.
The researchers concluded a wide vocabulary helped children absorb information across the curriculum.
They analysed the results of tests taken at the age of 16 by 6,000 children, all born in one week, from the 1970 British Cohort Study.
The findings showed those who had read often at the age of 10 and had been reading books and newspapers more than once a week aged 16 had performed better than those who had read less.
There was a 14.4% advantage in vocabulary, a 9.9% advantage in maths and an 8.6% advantage in spelling, the research found, once parents' background and reading habits were taken into account.
The study said: "The influence of reading for pleasure was greater than that for having a parent with a degree."
The total effect on children's progress of reading often - reading newspapers at age 16 and being a regular library user - was four times greater than the advantage of having a university-educated parent, the study suggested.
The Institute of Education also looked at the impact on test scores of having brothers and sisters and found that those youngsters with older siblings were less likely to do well, particularly in vocabulary.
It suggests this could be because children in larger families spend less time talking one-to-one with their parents and have less chance to develop their vocabulary skills.
There was less effect if children had younger brothers and sisters, although they may score lower on vocabulary, the study found.
Study author Dr Alice Sullivan said: "It may seem surprising that reading for pleasure would help to improve children's maths scores.
"But it is likely that strong reading ability will enable children to absorb and understand new information and affect their attainment in all subjects."
Speaking on BBC Radio 4's Today programme, she said: "It absolutely makes sense that you would expect reading for pleasure to improve children's vocabularies.
"But I think that that also does improve children's ability to take on new information and new concepts across the curriculum.
"A child who has a narrow vocabulary may constantly be coming across things they don't understand."

The multiple TT winner set the fastest time of the week in the Classic event on his Yamaha Superbike at 125.49mph.
Anglesey's Barry Lee Evans topped the Senior MGP board while home rider Michael Evans moved to the top of the Junior leaderboard.
Michael Evans' 119.228mph lap was the fastest Manx Grand Prix time so far.
Darryl Field leads the Newcomers' section after a lap of 115.09mph.
The session was cut short as mist fell on the mountain section with qualifying to continue on Friday evening with the first racing on Saturday.

The UK stage of the race comes to the city on 7 July.
Cycling enthusiast Rad Wagon is recruiting people to knit 3,000 miniature "Tour jerseys" and wool-covered bicycle wheels.
Schools and knitting groups have already offered to start knitting and the council was "interested", he said.
A similar "mini-jersey" idea is being promoted by Harrogate Borough Council for the Yorkshire stage of the race.
The public response to that was so overwhelming the council had to ask people not to send any more knitting to them.
"It's a bit copycat but we can do so much more," Mr Wagon said.
"The city's well-known for its knitters and 'yarn bombers' who cover everything from bikes to trees to lamp-posts. It's 'very Cambridge'.
"I think knitting is in Cambridge's DNA," he added.
Mr Wagon, a cycling skills and bicycle maintenance trainer from Outspoken Training in the city, said he was a fan not only of the Tour de France, but the cultural activities surrounding it.
"It isn't just a bike race. Its history is all about promoting your town and region and that's something we can do.
"The world's eyes will be on us and it's a chance for us to show that Cambridge can do things slightly differently, and perhaps slightly oddly," he said.
A knitting shop owner has offered to give knitting lessons and collect the tiny pullovers, Mr Wagon said.
A cycle shop in the city has also offered a collection of battered wheels which Mr Wagon hopes can also be turned into knitted decorations.
He said he was discussing suitable places his knitted bunting might go, with the city council.
Children who read for pleasure are likely to do better in maths and English than those who rarely read in their free time, research suggests.
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New Zealand racer Bruce Anstey continued to set the pace in the fourth qualifying session at the Isle of Man Festival of Motorcycling.
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A man who admits he "cannot knit a stitch" is hoping to cover the streets of Cambridge with knitted bunting and wool artwork during the Tour de France.