The so-called "association agreements" have been a focal point in the region's turmoil. In Ukraine, deadly protests broke out this winter when the president decided not to sign the EU deal under pressure from Moscow. The protests drove pro-Russian President Viktor Yanukovych from office, but drew the ire of Russia and pro-Russian militants in the country's east.
Here is a look at the agreements and their likely impact.
PURPOSE: The EU uses them to increase trade and political cooperation with non-members. The document provides an extensive blueprint for adopting the same rules, standards and practices that apply in the EU.
TRADE: Most importantly, the agreements remove almost all tariffs on imports into the EU of goods and services. The aim is to increase trade, growth and jobs. The signing countries should benefit because the EU, with 506 million people, is a very large market to do business with, and because tariffs are being removed more quickly by the EU than by the signing countries.
REFORM: Beyond trade, the agreements set out a broad reform agenda to modernize the economies of all three countries and increase business investment. The countries fell behind economically while part of the Soviet Union and its state-run economy, and are still lagging amid corruption, poor business climates and civil strife. The signers agree to adopt EU rules on government contracts, fair competition and the intellectual property rights on ideas and inventions. They also agree to strengthen the rule of law and independent courts. Adopting EU standards on products and food safety will protect consumers and make trade easier.
RUSSIA: As an alternative, Russia is holding out membership in a customs union with itself, Belarus and Kazakhstan. It has warned that if Ukraine signs the trade deal, it could lose its current free trade arrangement with Russia and face new tariffs on its products. It's not clear how far Russia will go. Russian authorities have blocked some Ukrainian imports. Russia blocked wine imports from Moldova ahead of a summit in November, when the country was first expected to sign the deal with the EU but did not. Russia barred wine from Georgia from 2006 until 2013.
HOLD THE GARLIC: Although most trade is being opened up, the EU kept in place restrictions on some agricultural products to protect its farmers from low-cost competition. Chickens from Ukraine and garlic from Moldova face import limits.
Ukraine won a 15-year transition period during which it can use tariffs to support its domestic auto industry from competition. Moldova will gradually eliminate protections for its dairy, pork, poultry and wine producers over 10 years.
NAME GAME: The agreement gives Ukrainian producers 10 years in which they can still use protected EU product names for alcohol such as Champagne and Cognac. It's seven years for cheese names such as feta, Parmigiano Reggiano and Roquefort.
FOLLOW THROUGH: Further trade opening will depend on progress in actually implementing the new rules and standards, by passing them into law through parliament and then enforcing those laws. If countries fail to follow through, progress could stall and that's not an unrealistic fear. Ukraine botched two aid deals with the International Monetary Fund in 2008 and 2010. Kiev pocketed the first payments of loan money and then did not follow through on reforms. The aid deals were cancelled and a third is just starting.
RATIFICATION: The EU has already lowered its tariffs on imports from Ukraine through Nov. 1 as a gesture of support. Since the agreement takes effect two months after ratification, Ukraine's parliament must ratify by late August and send the ratification documents to Brussels before the end of the month.
Otherwise, the tariffs will go up again Nov. 1 temporarily until Ukraine's lawmakers ratify the deal.