In Verse 18, Paul says, “God… hath reconciled us to Himself… and hath given to us the ministry of reconciliation.” Here we see that the people who have been given the ministry of reconciliation are the same people who have been reconciled to God. This cannot be limited to Paul and other leaders; it must include all believers, for we have all been reconciled.
Paul then defines the ministry of reconciliation as that which takes place when “ambassadors” say to the lost, “be ye reconciled to God” (v. 20). This means that the ambassadors proclaiming reconciliation in Verse 20 must consist of all the reconciled people who were given the ministry of reconciliation in Verse 18.
This also points out that, while “the world” has been reconciled to God (v. 19), the unsaved have not been reconciled in the same sense as believers, or else they would also be Christ’s ambassadors. The reconciling of the world is that which God gave Jews and Gentiles corporately, once the Jews had been cast away (Rom. 11:15), just as the Gentiles had been at the Tower of Babel.