Father and Son Agreeing for Our Salvation
Chapter 15 - Covenant of Redemption
Most Puritans saw the agreement between Father and Son for the Son to redeem mankind, as a separate covenant from the covenant of grace God made with the people He would save. This agreement is called the covenant of redemption.
Even before the fall of man into sin, God decided to satisfy divine justice and honor by Christ's atoning work, to reconcile man to God. The Father appointed, or ordained the Son (1 Peter 1:20) to be our "prophet (Deut 18:15), priest (Heb 3:1-2) and king (Ps 2:6)" (pg. 244). The Son accepts, and Isaiah 49 describes this discussion and agreement between Father and Son. The arrangement is for a specific people who Jesus will die for (limited atonement, or particular/definite redemption). Christ agreed to take on human nature, fulfill the covenant of works which Adam did not by keeping the law throughout His life, then die as an atoning sacrifice for our sins. The Father promised Christ would be equipped, rewarded, victorious, and effective in His task. The Spirit must have been involved in this covenant, given the closeness of the relations of the Persons, but there is no Scripture describing it. He was sent to apply our redemption, of course, but to what extent He was a "negotiating partner" of the formal covenant is a matter of dispute, so this was left out of the Westminster documents.
Christ's reward for keeping this covenant was that He would be glorified, rule the nations as King, and judge the world.
This covenant has many similarities with the covenant of grace God makes with man: grace is the motive, Christ the instrument, God elects, the elect benefit. But there are differences: there is no mediator in this covenant between Father and Son, no threat/warning for the Son, no involvement of man in it, the parties are equals, and man's consent was not required. Some preferred to say that this covenant was just the eternal and intra-Trinitarian aspect of God's covenant of grace to save men.
This covenant helps explain John 14:28, where Jesus says, "My Father is greater than I."