Exceeding the quota meant the producer state had to pay what was called a "super levy" to the EU.
The main reason for ending milk quotas was the large increase in dairy product consumption in recent years, especially on the world market.
Read also:
• Fonterra 'on track' to hit payout
• Mood likely to be brighter at Fonterra's board meeting
As the increase was projected to continue in future, the quota regime was preventing EU producers from responding to increased demand.
At close to 55 billion ($79.2 billion), the dairy sector is 15 per cent of total EU agricultural output.
Germany is the largest producer, followed by the Netherlands, Denmark and Poland. Ireland has ambitions to increase its production by 50 per cent by 2020.
Fonterra's standpoint is that anything that improves the transparency of international pricing of dairy product is a move in the right direction, even though the likely outcome will be increased production coming on to the market and more competition.
ANZ rural economist Con Williams said anticipated extra production from Europe may have played a part in weaker prices at the last GlobalDairyTrade auction.
Williams said it also looked like most buyers appeared happy their second-quarter requirements had been filled, so had taken to the sidelines.
"With uncertainty over European milk supply and what they will turn that into, a lot of buyers seem to be taking a wait-and-see approach," Williams said.
Signals from the futures market are pointing to weaker physical prices at tomorrow's GlobalDairyTrade auction.
Lower prices are likely to reflect a number of factors, among them increased supply going on to the GDT platform from Fonterra and the realisation the impact of New Zealand's drought on production is not going to be as drastic as first thought.
Williams said it looked like the market would continue to backtrack after posting some big gains in February.
The next three or four auctions would be critical for Fonterra when it formulates its farmgate milk price forecast for 2015/16, which is expected to happen at the end of May.
In New Zealand, about 95 per cent of dairy production is exported, while in the EU about 90 per cent is consumed domestically.
EU Commissioner for Agriculture and Rural Development Phil Hogan said the abolition of quotas would be a challenge and an opportunity.
"It is a challenge because an entire generation of dairy farmers will have to live under completely new circumstances and volatility will surely accompany them along the road," he said. "But it certainly is an opportunity in terms of growth and jobs."
Milking time
• EU is dismantling its dairy quota system.
• Farmers can produce as much as they want.
• Quota system was introduced to curb overproduction.
• Main reason for ending system is the increase in consumption.
• €55 billion sector represents 15% of EU agricultural output.
• About 90% of production is consumed domestically.