In an interesting article published in the Catholic Biblical Quarterly, "Creation's Renewal in the Gospel of John" by Jeannine Brown of Bethel Seminary, San Diego, we find the following about the theology underlying the use of τετελεσται in John19: 28, 30:
The Completion of God's Work: The Sabbath
A number of Johannine scholars have noted the theme of God's work coming to completion in Jesus, especially in connection with 19:28, 30. In these verses, the author uses τελεω to indicate completion: "when Jesus knew that all was now finished [τετελεσται] . . ." (19:28) and "[Jesus] said, 'It is finished [τετελεσται]" (19:30). As Raymond E. Brown indicates in his discussion of 19:28, the motif of God's work being fulfilled in Jesus begins earlier in the Gospel and is especially apparent in chaps. 4-5, where Jesus clarifies his work in relation to God's work. "My food is to do the will of him who sent me and to complete [τελειωσω] his work [αυτου το εργον]" (4:34); "The works that the Father has given me to complete [τελειωσω], the very works [αυτα τα εργα] that I am doing, testify on my behalf that the Father has sent me" (5:36). Given these narrative connections in John between chaps. 4-5 and 19:28, 30, along with the focus in Genesis 1 on the work of God in creation (see Gen 2:2: "God rested from all the work [LXX: τα εργα] that he had done in creation"), it is probable that the Johannine notion that Jesus comes to complete God's work echoes the creation story of Genesis.
Implied in this Johannine motif of the completion of God's work in the Messiah is the assumption that God's work is not yet completed, though the Genesis passage that is echoed (Gen 2:1-3) explicitly communicates the completion of God's work with the resulting rest from that work. The author of John expresses that Jesus' work, which culminates in the cross (19:30), completes the Father's work, ushering in the Sabbath of God's full rest. The reader hears this idea in the motif of τελεω, the explicit indication that the Father is still working (with Jesus joining that work), and in the signalling of the Sabbath's arrival upon Jesus' death (19:31).
In 5:17, Jesus answers antagonism over his healing activity on the Sabbath with these words, "My Father is still working, and I also am working." The idea that God continues to work, even on the Sabbath, was present in Jewish reflections of the rabbinc period and possibly Jewish traditions predating John. For example, Gen. Rab. 11.10 qualifies Gen 2:2 by indicating that "it was from the work of the world that he rested. But he did not rest from the work involving the wicked or from the work involving the righteous. But he continued to labor with these and with those." Both Genesis Rabbah and John qualify (albeit in different ways) the Sabbath rest of God in Gen 2:2-3 without negating it. In John, the work of God is understood as coming to completion at the cross (19:28, 30). Thus the eschatological Sabbath begins.
It is important in this regard that immediately after Jesus' words from the cross, "It is finished," John mentions that the Sabbath is about to begin (19:31). This connection may once again echo Genesis, where the completion of God's creative work culminates in the seventh day of God's rest (Gen 2:2-3). The Sabbath, which is clearly a temporal indicator on the story level in John, it is a theological signal at the level of author and reader. The Sabbath as a theological signal combines with the notion of Jesus' doing the Father's work (4:34; 5:17, 36) and bringing it to completion at the cross (19:28, 30) to usher in the Sabbath rest of creation's renewal. These various motifs come at a climactic moment of the Gospel, leading into 20:1, where the author turns to the resurrection narrative: "Early on the first day of the week [σαββατον]." The arrival of the first day of the week caps the various allusions of the work of God (in creation) that has now come to completion in Jesus' death, ushering in the Sabbath rest and re-creation. (Jeannine K. Brown, "Creation's Renewal in the Gospel of John," CBQ 72/2 (April 2010), pp. 275-90, here, pp. 284-86)
For more on τετελεσται and the theology of John 19:30, see: