A study of just over 1,000 women found the risk doubles if women go to sleep on their backs in the third trimester.
The study looked into 291 pregnancies that ended in stillbirth and 735 women who had a live birth.
Researchers say the position in which women fall asleep in is most important - and they should not worry if they are on their back when they wake up.
About one in 225 pregnancies in the UK ends in stillbirth and the study authors estimate that about 130 babies' lives a year could be saved if women went to sleep on their side.
The MiNESS study, published in the British Journal of Obstetrics and Gynaecology (BJOG) is the biggest of its kind, and confirms findings from smaller studies in New Zealand and Australia.
Is waking up on your back a problem?
Prof Alexander Heazell, clinical director at the Tommy's Stillbirth Research Centre at St Mary's Hospital in Manchester, who led the research, advises women in their third trimester to sleep on their side for any episode of sleep, including daytime naps.
"What I don't want is for women to wake up flat on their back and think 'oh my goodness I've done something awful to my baby'.
"The question that we asked was very specifically what position people went to sleep in and that's important as you spend longer in that position than you do in any other.
"And also you can't do anything about the position that you wake up in but you can do something about the position you go to sleep."
Tips for going to sleep on your side
- Put a pillow or pillows behind your back to encourage side-sleeping
- If you wake during the night, check your position and go back to sleep on your side
- Pay the same attention to sleep position during the day as you would during the night
- If you wake on your back during the night, don't worry, just roll on to your side
- The study didn't find a difference in risk between right or left side
Researchers can't say for certain why the risk of stillbirth is increased - but there is a lot of data that suggests when a woman is lying on her back, the combined weight of the baby and womb puts pressure on blood vessels which can then restrict blood flow and oxygen to the baby.
Edward Morris, from the BJOG, said the new research was "extremely welcome" .
"This is an important study which adds to the growing body of evidence that sleep position in late pregnancy is a modifiable risk factor for stillbirth."
The pregnancy charity Tommy's has started a campaign to raise awareness of the study and to encourage women to sleep on their side.
Michelle Cottle's baby Orla was stillborn at 37 weeks in 2016 after a healthy pregnancy where there were no signs that anything was wrong.
She writes a blog "Dear Orla" and hears from women who have been through the same experience.
Michelle, whose daughter Esme was born a year later, says practical advice like this for mothers is important to make them feel more in control.
"I really think it helps to empower people, as it feels like something you can go away and do with the hope of having a healthier pregnancy and a better outcome than sadly lots of people do have.
"I look back now and I actually feel quite traumatised by my (second) pregnancy because it was a bit like living your worst nightmare every single day.
"Every time there's maybe a quiet moment and you don't know whether your baby is alive or not is absolutely terrifying.
"Night-time is the worst as well because a lot of people would say they believe that their baby died maybe when they were sleeping. I think that's really scary because you have to sleep.
"So I think having clear things that can help you feel a bit more in control is really important for women."
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