The carmaker climbs from fourth place in the 2014 rankings to take the top spot from Sony, which had been top of the rankings in both 2013 and 2014.
The second most reputable company in the EU is Lego - which is also the best reputation among UK respondents.
For its 2015 Europe RepTrak 100, the Reputation Institute questioned 15,000 members of the public across France, Germany, Italy, Spain and the UK about perceptions of the world's 100 most visible companies.
The rest of the EU-wide ranking's top five also includes (in descending order) Sony, Samsung and The Walt Disney Company. The top ten is then completed by Daimler, Canon, Google, Ferrero and Michelin.
The UK top ten is: Lego, Kellogg's, Rolls-Royce, Sony, Samsung, Rolex, BMW Group, Volkswagen, The Walt Disney Company and Amazon.
A different firm comes top of each market's list: Daimler comes top among French respondents, while BMW Group is on top in Germany, Ferrero in Italy and The Walt Disney Company in Spain.
There are seven areas on which companies are scored making up the rankings are: products/services, innovation, workplace, governance, citizenship, leadership and financial performance. While BMW does not come on any of these measures - the single biggest score is Rolex for products/services - it is in the top four companies in all seven of the categories.
According to Reputation Institute, consumers are more likely to buy from or recommend a company with a higher reputation, and are also more than twice as likely to give reputable companies the benefit of the doubt in a crisis.
A survey commissioned by PRWeek for this month's corporate reputation issue found that the Co-operative Group was the UK's most trusted company.