HUNSTEIN, Chief Justice.

In 1993, a jury found appellant Joseph M. Barnes guilty of malice murder, two counts of felony murder, and armed robbery and recommended a sentence of death for the murder. The trial court sentenced Barnes to death for the murder and also imposed a consecutive life sentence for the armed robbery. This Court affirmed Barnes' convictions but vacated the death sentence and remanded to the trial court for a new sentencing hearing based on our conclusion that the trial court had improperly restricted the scope of mitigating evidence presented at the sentencing phase of Barnes' trial. See Barnes v. State, 269 Ga. 345(27), 496 S.E.2d 674 (1998). On remand, Barnes and the State entered into a sentencing agreement under which Barnes accepted a sentence of life without parole and the State agreed to withdraw its notice of intent to seek the death penalty.1 The trial court accepted the agreement at a hearing on November 16, 1999 and sentenced Barnes to life without parole on his malice murder conviction. On August 30, 2011, Barnes, proceeding pro se, filed a motion for out-of-time appeal. Barnes appeals following the denial of his motion, and we affirm.

In prior cases, we have examined enumerations of error related to the validity of a sentencing agreement like Barnes' under the same legal standards applicable to guilty pleas. See Hinely v. State, 275 Ga. 777, 783(5), 573 S.E.2d 66 (2002) (holding in case involving sentencing agreement similar to Barnes' that "the prospect of a greater sentence is not coercion that prevents the decision to plead guilty, or to accept a certain lesser sentence, from being free and voluntary"); Brantley v. State, 268 Ga. 151(1), 486 S.E.2d 169 (1997) (analyzing claim of ineffective assistance of counsel in connection with sentencing agreement under standard applicable to ineffective assistance claim in context of guilty plea). Likewise, in reviewing the issue on appeal in this case, we turn for guidance to our cases addressing the availability of an out-of-time appeal from a judgment and sentence entered on a guilty plea. "It is well established that a criminal defendant has no unqualified right to file a direct appeal from a judgment of conviction and sentence entered on a guilty plea." (Citation and punctuation omitted.) Brown v. State, 290 Ga. 321(1), 720 S.E.2d 617 (2012). "[A]n appeal will lie ... only if the errors asserted on appeal can be resolved by facts appearing on the face of the record, and the denial of a request for out-of-time appeal is proper if an examination of the record reveals no merit to the claimed errors." (Citations and punctuation omitted.) Adams v. State, 285 Ga. 744(1), 683 S.E.2d 586 (2009).

Barnes maintains that the sentencing agreement should be invalidated because the trial court imposed multiple life sentences for the same offense, contrary to the terms of the sentencing agreement and Georgia law.2 The record contradicts Barnes' contentions. Under the sentencing agreement, Barnes agreed to accept a single sentence of life without parole for malice murder, and that is the sentence the trial court imposed. The two felony murder convictions always stood vacated by operation of law. Williams v. State, 270 Ga. 125, 126(4), 508 S.E.2d 415 (1998) ("When the jury returns guilty verdicts on both felony murder and malice murder charges in connection with the death of one person, it is the felony murder conviction ... that is simply surplusage and stands vacated by operation of law") (citations and punctuation omitted). Because our prior decision affirmed Barnes' conviction and life sentence for armed robbery, the sentencing agreement could not and did not purport to address his sentence for that offense. Barnes' argument to the contrary notwithstanding, the armed robbery conviction did not merge into his conviction for felony murder with armed robbery as the underlying felony. Where, as here, a felony murder conviction is vacated by operation of law, "there is no felony murder [conviction] into which the underlying felony can merge." Malcolm v. State, 263 Ga. 369, 373(5), 434 S.E.2d 479 (1993). Nor did Barnes' conviction for armed robbery merge into the malice murder conviction. See Culpepper v. State, 289 Ga. 736(2)(b), 715 S.E.2d 155 (2011).

Because Barnes' challenges to the validity of the sentencing agreement can be resolved against him on the record, the trial court did not err in denying his motion for an out-of-time appeal. See Upperman v. State, 288 Ga. 447(1), 705 S.E.2d 152 (2011); Adams, supra, 285 Ga. at 748-749, 683 S.E.2d 586.

Judgment affirmed.

All the Justices concur.