Fortinbras is in a similar situation to Hamlet: he seeks to reclaim a land his father lost before dying. He is one of Hamlet's foils, however; instead of overthinking his course of action, Fortinbras proves to be a man of direct action, aligning an army to support his efforts. Hamlet recognizes the strengths of Fortinbras as a leader, too, remarking,

To be great
is not to stir without great argument
but greatly to find quarrel in a straw
when honors at the stake.

When Fortinbras charges onto the scene of so much death at the end of the play, he arrives just after Hamlet gives his blessing that this is the man who deserves to be the next king. Fortinbras provides much respect for the fallen Hamlet, allowing for a soft closure on this tragic loss of life:

For he was likely, had he been put on,
To have proved most royal; and for his passage,
The soldiers' music and the rites of war
Speak loudly for him.

Fortinbras acknowledges that his success rests on the death of Hamlet, though not by his own hands, and he treats him as an honorable fallen hero while staking his own personal claim on the throne.

Fortinbras is a minor figure in the play, but he is present at critical junctures, which is important to note. We hear of him in the beginning of the play as an ambitious young man. We also hear of him when Hamlet meets him on his journey, and Hamlet learns that Fortinbras is about to attack Poland. Moreover, Hamlet feels diminished that he is not decisive like Fortinbras. Hamlet still has not avenged his father’s death. Finally, Fortinbras comes at the end of the play to take the throne in view of the death of Claudius and Hamlet. Here is what Fortinbras says

Let us hast to hear it
And call the noblest to the audience.
For me, with sorrow I embrace my fortune.
I have some rights of memory in this kingdom,
Which now to claim my vantage doth invite me.

I should also point out that Fortinbras also honors Hamlet at the end of the play. He points out that Hamlet is royal. He speaks these words:

Bear Hamlet like a soldier to the stage,
For he was likely, had he been put on,
To have proved most royal . . .

All evidence, therefore, points to the ironic fact that Fortinbras becomes the king. And he shows his power by honoring Hamlet.

The play of Hamlet comes full circle with the end of Act 5 and Fortinbras's arrival at the Danish court.  In Act 1 we hear about his plans to try to attack Denmark in order to regain the lands lost by his father to King Hamlet many years earlier.  In Act 5, Fortinbras is in Denmark on his return from a battle in Poland.  When he arrives at the court he is confronted with the sight of four dead bodies:  King Claudius, Queen Gertrude, Laertes, and Prince Hamlet.  It would seem that with no one in the royal family to take the throne, it is going to come to Fortinbras by default.  It is actually Hamlet's final words that help to solidify this result.  He tells Horatio that he "sets his election lights on Fortinbras."  As Denmark is an elected monarchy, this will help ensure that Denmark is left in the hands of a royal person whom Hamlet knows is capable of decisive action (as we learn from Hamlet's reaction to seeing him back in Act 4.)  Fortinbras hears the story of how these deaths came to be from Horatio, and Fortinbras responds with the fact that "it is with sorrow (for all the needless death) I embrace my fortune."  He solidifies the justice of his taking the crown when he says, "I have some rights of memory in this kingdom / Which now to claim my vantage doth invite me."  Fortinbras acknowledges that Hamlet may have been a good king had be had throne, and he ensures that Hamlet will be given a funeral fitting a king.  The only problem with all of this is that now Denmark is the hands of a foreign ruler.  What Hamlet was trying to do -- rid the Danish throne of corruption and evil -- is done, but the results are not what anyone would have wished.