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Unconditional election (also known as unconditional grace) is a Reformed doctrine relating to predestination that describes the actions and motives of God prior to his creation of the world, when he predestined some people to receive salvation, the elect, and the rest he left to continue in their sins and receive the just punishment, eternal damnation, for their transgressions of God's law as outlined in the Old and New Testaments of the Bible. God made these choices according to his own purposes apart from any conditions or qualities related to those persons.
The counter-view to unconditional election is conditional election, the belief that God chooses for eternal salvation those who he foreknows will exercise their free will to respond to God's prevenient grace with faith in Christ.
In Calvinist (Reformed) theology, unconditional election is considered to be one aspect of predestination in which God chooses certain individuals to be saved. Those elected receive mercy, while those not elected, the reprobates, receive justice without condition. This unconditional election is essentially related to the rest of the TULIP doctrinal outline and hinges upon the supreme belief in the absolute sovereignty of God over the affairs of man. God unconditionally elects certain people even though they are sinful as an act of his saving grace apart from the shortcomings or will of man. Those chosen have done nothing to deserve this grace.
In Calvinist and some other churches (Waldensians, Katharoi, Anabaptists, Particular Baptists, etc.) this election has been called "unconditional" because his choice to save the elect does not depend on anything inherent in any person chosen, on any act that a person performs or on any belief that a person exercises. Indeed, according to the doctrine of total depravity (the first of the five points of Calvinism), the influence of sin has so inhibited the individual's volition that no one is willing or able to come to or follow God apart from God first regenerating the person's soul to give them the ability to love him and take part in the salvation process. Hence, God's choice in election is and can only be based solely on God's own independent and sovereign will and [not] upon the foreseen actions of man.
Scholastic Calvinists have sometimes debated precisely when, relative to the decree for the Fall of man, God did his electing – see supralapsarianism and infralapsarianism – though such distinctions are not often emphasized in modern Calvinism.
The Reformed position is frequently contrasted with the Arminian doctrine of conditional election in which God's eternal choice to save a person is conditioned on God's certain foreknowledge of future events, namely, that certain individuals would freely exercise faith and trust in response to God's offer of salvation. The Arminian doctrine agrees that the influence of sin has so inhibited the individual's volition that no one is willing or able to come to or follow God, but the Arminian doctrine of prevenient (or "enabling") grace is considered sufficient to enable a person to believe and repent before regeneration. Based upon God's certain foreknowledge of individual human response to the gospel of Jesus Christ, God justly and sovereignly elected individuals to salvation.
The doctrine was first articulated and popularized by 4th century Church Father Augustine of Hippo during his debates with Pelagius, and he taught that saving grace is bestowed by God on the elect according to his sovereign decrees. Few later theologians prior to the Reformation would take up this idea. However, prominent exceptions include Thomas Aquinas. 
Unconditional election was first codified in the Belgic Confession (1561), re-affirmed in the Canons of Dort (1619), which arose from the Quinquarticular Controversy, and is represented in the various Reformed confessions such as the Westminster Standards (1646). It is one of the five points of Calvinism and is often linked with predestination. Today it is most commonly associated with the Reformation teachings of John Calvin known as Calvinism.
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A number of passages are put forth to support the doctrine, including (quotations are from the KJV):
Some biblical passages are put forth as evidence that human volition, not just divine action, plays a central role in salvation (see conditional election):
Calvinists generally understand the former passages as giving a window into the divine perspective and the latter passages as speaking from the human perspective in calling people to work out the salvation God has given them.