The study, by the Scottish Centre for Social Research, found that 90 per cent of those surveyed said the scheme was improving the eating habits of P1 and P2 pupils, and 60 per cent also said children were eating more fresh fruit and vegetables for lunch.
Grapes, melons, bananas, apples and strawberries were the most popular.
Tomatoes, oranges, carrots, red peppers and dried fruit were relatively unpopular because of their size, the need to peel them, and their stones and pips.
The researchers add that the initiative should be seen in the context of the wider Hungry for Success policy and the push for health-promoting schools.
About 88 per cent of schools said they had made links between the taught curriculum and the free fruit initiative, including health education topics and environmental studies.
For the past two years, the Executive has provided pound;2 million a year to pay for all P1 and P2 children to receive free fruit three times a week.
Some authorities were already providing free fruit. Glasgow has offered free fruit to all primary and nursery children five times a week since 2001, while others had introduced fruit into tuck shops. Many call for the initiative to be extended to cover more pupils (including secondary), operate more frequently, offer larger portions, and involve pupils in preparing the fruit.
Some authorities complained that the money from the Executive was not always adequate, especially if they were to include more pupils and improve other elements of the scheme, such as providing a wider variety of fruit.
Some said they were using some Hungry for Success funding to run the free fruit scheme so they could provide a wider range of fruit or include other pupils beyond P1 and P2. Some schools reported extra costs in including P2 pupils where they had composite classes.
A minority said the initiative was disruptive for schools.
The report says: "The main hurdle that had to be overcome was the time teachers had to spend on administering the initiative and the consequent loss of class time with the children. In some areas there was initial resistance from teaching staff to the scheme, the problem scarcely ameliorated by the recommendation that the fruit should be eaten in the classroom rather than in the playground. However, local authority respondents stressed that they had liaised with school staff to convince them of the value of the initiative."
Other concerns were that fruit was not always of the highest quality, storage was not always adequate, and that school staff should be paid to compensate them for preparing and distributing the fruit.
The majority reported that initial problems had been overcome and that minor difficulties were a price worth paying as the benefits of the initiative far outweighed the negatives.
Not one local authority thought the initiative should not continue and only five schools (1 per cent) called for the end of the initiative.
Almost all authorities reported that they tried to supply seasonal fruit, although five cited cost as a problem. Most authorities did not supply organic fruit and vegetables because of their higher cost andor lack of availability.
About three-quarters of local authorities reported fruit wastage of less than 20 per cent, although one respondent thought that 60 per cent of vegetables in some schools were being wasted.
Given the very different areas and school rolls covered by the local authorities, costs of operating the initiative ranged from about pound;12,000 to pound;1 million a year.