The Lord Jesus, in His human nature thus united to the divine, was sanctified and anointed with the Holy Spirit, above measure, having in Him all the treasures of wisdom and knowledge; in whom it pleased the Father that all fulness should dwell; to the end that, being holy, harmless, undefiled, and full of grace and truth, He might be thoroughly furnished to execute the office of a mediator and surety. Which office He took not unto Himself, but was thereunto called by His Father, who put all power and judgment into His hand, and gave Him commandment to execute the same. - WCF 8.3
"Only one human being has ever kept the covenant of works. That person was Jesus. His work as the second or new Adam fulfilled all the terms of our original covenant with God. His merit in achieving this is available to all who put their trust in Him." - R. C. Sproul
Resources
The Mediator of the Covenant, Described in His Person, Natures and Offices by William Whitaker
How Christ Has Fulfilled the Function of Redeemer to Acquire Salvation for Us by John Calvin
To Fulfill All Righteousness by Knox Chamblin
Jesus’ Baptism: To Fulfill All Righteousness by Ligon Duncan
The Covenant of Grace with Abraham, Fulfilled by Ligon Duncan
Obedience - Jesus Christ Fulfilled His Father's Redemptive Will by J. I. Packer
Why Did Jesus Need the Holy Spirit? by Nick Batzig
Gifts of Grace for Jesus? by Nick Batzig
Christ, Our Surety by Richard Sibbes
How Does Christ “Fulfill” Historical Remarks? by Ruben Zartman
How Did Christ Fulfill The Covenant Of Works As The Last Adam? by R. Scott Clark
Through the Westminster Confession, Chapter 8.2, 3 by William VanDoodewaard
Hallelujah! Jesus Fulfilled the Law for Us by Scotty Smith
The Holy Spirit: Jesus’s Closest Companion by Dr Sinclair B Ferguson
Why Jesus Needed the Holy Spirit by Mark Jones
God's Obedient Son by Nick Batzig
How Jesus Transforms the Ten Commandments – The Covenant Lord Fulfils the Law (.pdf) by Edmond P. Clowney
The Nature of the Suretyship of Jesus Christ During the Old Testament by Wilhelmus Brakel
Work of the Holy Spirit in and on the human nature of Christ by John Owen
Did Christ as the Incarnate Mediator, Fulfill the Law and All Righteousness for Himself or for Those He Came to Save? by John Owen
eBooks
The Fountain of Life: a display of Christ in his glory (eBook) by John Flavel
Christ Set Forth (eBook) by Thomas Goodwin
The Heart of Christ in Heaven (eBook) by Thomas Goodwin
The Glory of Christ (eBook) by John Owen
The Lord of Glory (eBook) by B. B. Warfield
Spiritual Union & Communion (eBook) by A. W. Pink
The Virgin Birth by J Gresham Machen
On the Incarnation by St. Athanasius
Cur Deus Homo (Why God Became a Man) by St. Anselm
Christ: A Complete Saviour or the Intercession of Christ and Those Who Are Privileged in It (eBook) by John Bunyan
Multimedia
The Active Obedience of Christ by R. C. Sproul
Of Christ the Mediator (Ch.8, Sec.3-4) by Greg Bahnsen
The Active Obedience of Christ by J. Gresham Machen
Christ’s Active and Passive Obedience by Louis Berkhof
To Fulfill All Righteousness by Rev. Jason Van Bemmel
Fulfill All Righteousness by Dr. William D. Dennison
Books
Jesus the Son of God by D A Carson
Dialogue on the Two Natures in Christ by Peter Vermigli
The Word Enfleshed by Oliver Crisp
What is the Incarnation by William Evans
The Son of God and New Creation by Graeme Goldsworthy
The God Who Became Human by Cole Graham
The Person of Jesus by J. Gresham Machen
The Christian’s Pocket Guide to Jesus Christ by Mark Jones
The Person of Christ by Donald MacLeod