Yes!

With some restrictions.

Foreigners may obtain direct ownership of property in the interior of Mexico. Foreigners cannot acquire direct ownership of residential property within the area 100 kilometers from the border and 50 kilometers from the coastline. This area is known as the restricted zone. It is possible, however, to acquire beneficial rights to use, improve, and enjoy property in the restricted zone through a Bank Trust or Fideicomiso authorized by the Mexican Government under the Ministry of Foreign Affairs.

The Fideicomiso is established for a 50 year renewable term and grants the beneficiary the right to use, rent, modify, or sell the property. An advantage of the bank trust is the avoidance of probate upon the death of the beneficiary when a substitute is named. Property acquired for commercial use by foreigners may be owned without the need for a bank trust, provided that the property is held in a Mexican corporation. Depending on the type of business, it is often possible for a foreigner to own 100% of the Mexican corporation. In a typical transaction, a preliminary sales agreement will be used.

This is like an agreement to agree and is subject to a formal sales agreement which will be executed at closing by a Notario Publico. The preliminary agreement should provide for a price and terms -- generally, cash as financing is not readily available -- and a closing date conditioned on the issuance of the trust permit if necessary.

Other due diligence contingencies may be negotiated, but they are not customary.   Escrow as it is known in the United States is not used in Mexico, and real estate salespeople are not licensed or regulated as they are in the United States, so be careful of making any deposits up front. Escrow services are available through the Mexico Division of Stewart Title, Houston, Texas.  

Real estate transactions in Mexico are "closed" by a Notario Publico, an official, highly respected government lawyer who acts as a neutral intermediary. Among other things, the notary is responsible for formalization of the final real estate contract, collection of transfer and capital gains taxes and recordation of the transfer with the Public Registry. The notary is not your lawyer, however, and as with any investment, you may want to seek independent Mexican or U.S. legal counsel before proceeding.