Hanson Building Materials, Inc., and Hanson Australia PTY Limited (collectively “Hanson”) appeal an order compelling arbitration of a lawsuit against Joel Pennington. We affirm.

I.

Pennington is a former employee of Hanson’s. From 1999 to 2001 Pennington was stationed in Australia, during which time Hanson paid Pennington’s foreign income taxes under a “tax equalization policy.” On termination of his employment with Hanson, Pennington and Hanson entered into a Confidential Separation Agreement and Full Settlement of Claims (“Separation Agreement”), which contained a mandatory arbitration clause. 1

*578 Hanson later sued Pennington under the tax equalization policy for the return of foreign tax refunds that were paid to Pennington. Pennington counterclaimed for breach of the Separation Agreement.

Each party moved for compelled arbitration of the claim against it pursuant to the Separation Agreement’s arbitration provision. The district court issued an order dismissing and compelling arbitration of both claims. The court determined that Pennington’s counterclaim for breach of the Separation Agreement was plainly governed by the Separation Agreement and therefore subject to arbitration. The court further held that Hanson’s claim under the tax equalization policy was subject to the arbitration provisions of the Separation Agreement because the Separation Agreement superseded the tax equalization policy. The court relied on the following language from paragraph 14 of the Separation Agreement:

Employee (Pennington) fully under stands and acknowledges that this Agreement ... constitutes the full resolution and satisfaction of all duties and obligations owed by the Company (Hanson) and supersedes any other agreement, whether express or implied, regarding the terms and conditions of his employment.

The parties agree that Pennington’s counterclaim for breach of the Separation Agreement is subject to arbitration. Hanson contends, however, that its claim for the return of foreign tax refunds under the tax equalization policy is not covered by the Separation Agreement and therefore is not subject to arbitration. Hanson argues that the Separation Agreement did not supersede the tax equalization policy.

II.

We review de novo the district court’s grant of a motion to dismiss and to compel arbitration. Pennzoil Exploration & Prod. Co. v. Ramco Energy Ltd., 139 F.3d 1061, 1065 (5th Cir. 1998). “A party cannot be required to submit to arbitration any dispute which he has not agreed so to submit.” United Steelworkers of Am. v. Warrior & Gulf Nav. Co., 363 U.S. 574, 582, 80 S.Ct. 1347, 4 L.Ed.2d 409 (1960). In determining whether the parties have agreed to arbitrate, we ask (1) whether a valid agreement to arbitrate between the parties exists and (2) whether the dispute in question falls within the scope of that arbitration agreement. PaineWebber Inc. v. Chase Manhattan Private Bank (Switzerland), 260 F.3d 453, 462 (5th Cir. 2001). “In doing so, we must bear in mind the strong federal policy favoring arbitration and resolve any ambiguity as to the availability of arbitration in favor of arbitration.” Id.

The parties agree that the Separation Agreement contains a valid arbitration clause covering all disputes under the Separation Agreement. We must determine, therefore, whether Hanson’s claim under the tax equalization policy falls under the Separation Agreement.

The plain language of paragraph 14 of the Separation Agreement contains two distinct agreements. First, the parties agreed that the Separation Agreement “constitutes the full resolution and satisfaction of all duties and obligations owed by the Company.” Second, they agreed that the Separation Agreement “supersedes any other agreement, whether express or implied, regarding the terms and conditions of his (Pennington’s) employment.” This second agreement is not somehow subsumed by the first, as argued by Hanson.

The tax equalization policy is certainly an “agreement ... regarding the terms and conditions of [Pennington’s] employment.” Therefore, it was superseded by the Separation Agreement. Any dispute now arising under the tax equalization pol *579 icy is therefore governed by the Separation Agreement and subject to arbitration.

AFFIRMED.