p>Official advice is to breastfeed exclusively for the first six months of life.
Experts say women should still heed this recommendation, although it is under review.
In the study, in JAMA Pediatrics, giving solids earlier than six months had benefits for mum and baby.
The babies slept for longer and mothers reported improved quality of life.
The study, by King's College, London, and St George's, University of London, surveyed 1,303 three-month-olds, and divided them into two groups.
One group was solely breastfed for six months, the other group was given solid foods in addition to breast milk from the age of three months.
Parents then filled in online questionnaires every month until their baby was 12 months old, and then every three months until they were three years old.
The study showed that infants in the group who ate solids as well as breast milk:
Although the findings were significant, the differences between the solids group and the control group were not huge.
Babies on earlier solids slept for up to 16 minutes longer per night, potentially giving parents about two extra hours of sleep per week.
Co-author of the study Dr Michael Perkin, from St George's, University of London, says small differences generated large benefits for parents. "Given that infant sleep directly affects parental quality of life, even a small improvement can have important benefits."
More significantly, the group of babies on early solids reported half the rate of the type of sleep problems, such as crying and irritability, which make it less likely that parents are going to get back to sleep.
The NHS and World Health Organization currently advise to wait until around six months before introducing solid foods, but these guidelines are currently under review.
Experts say babies should not have solid foods, at the earliest, before the end of four months.
Despite the official advice, 75% of British mothers introduced solid food before five months, with a quarter (26%) citing infant night-time waking as the reason for their decision, according to the Infant Feeding Survey of 2010.
Prof Gideon Lack from King's College, London, said: "The results of this research support the widely held parental view that early introduction of solids improves sleep.
"While the official guidance is that starting solid foods won't make babies more likely to sleep through the night, this study suggests that this advice needs to be re-examined in light of the evidence we have gathered."
Responding to the study, Prof Mary Fewtrell, nutrition lead at the Royal College of Paediatrics and Child Health, pointed out that guidelines for infant feeding are currently being reviewed.
She said: "These are interesting findings from a large randomised controlled trial.
"At the RCPCH, we recommend that mothers should be supported to breastfeed their healthy-term infant exclusively for up to six months, with solid foods not introduced before four months.
"However, the evidence base for the existing advice on exclusive breastfeeding is over 10 years old, and is currently being reviewed in the UK by the Scientific Advisory Committee on Nutrition.
"We expect to see updated recommendations on infant feeding in the not too distant future."
What to feed babies in the first six months of life can be controversial, with many mothers feeling judged if they are unable to breastfeed successfully, and guilty if they introduce bottles or solids.
Last month, the Royal College of Midwives responded to the pressure felt by new mothers by publicly stating new guidelines for midwives to respect a woman's choice not to breastfeed.
The study on solids was part-funded by the Food Standards Agency, which was also looking at how allergies develop in babies.
An FSA spokesperson said: "We are encouraging all women to stick to existing advice to exclusively breastfeed for around the first six months of age.
"If there is any doubt about what's best for your baby, please seek advice from your doctor or health professional."
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