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The Player's Handbook, Chapter 9, states about attack rolls:

The ability modifier used for a melee weapon attack is Strength

A bit later on it also states about melee attacks:

Instead of using a weapon to make a melee weapon attack, you can use an unarmed strike: a punch, kick, head-butt, or similar forceful blow (none of which count as weapons). On a hit, an unarmed strike deals bludgeoning damage equal to 1 + your Strength modifier. You are proficient with your unarmed strikes.

I'm not sure whether an unarmed strike is considered a "melee weapon attack."

For a basic unarmed strike (i.e. no Monk, Tavern Brawler or anything else that enhances unarmed strikes), is only the proficiency bonus added to the attack roll, or is the Strength modifier also added?

Clearly the Strength modifier is added to the damage, but I'm asking about the attack roll.

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Attack roll for unarmed strikes = d20 + proficiency bonus + Strength modifier.

Unarmed strikes are, in fact, melee weapon attacks - even though they're not made with a weapon. This is clarified in the Sage Advice Compendium:

What does “melee weapon attack” mean: a melee attack with a weapon or an attack with a melee weapon?

It means a melee attack with a weapon. Similarly, “ranged weapon attack” means a ranged attack with a weapon. Some attacks count as a melee or ranged weapon attack even if a weapon isn’t involved, as specified in the text of those attacks. For example, an unarmed strike counts as a melee weapon attack, even though the attacker’s body isn’t considered a weapon.

Here’s a bit of wording minutia: we would write “melee-weapon attack” (with a hyphen) if we meant an attack with a melee weapon.

This is also supported by the fact that the rules on unarmed strikes are stated in the the "Melee Attacks" section of the rules; the wording is simply clarifying that if you want to make a melee weapon attack without a weapon, you can use an unarmed strike to do so.

Jeremy Crawford has also reiterated many times on Twitter that despite not using weapons, unarmed strikes are melee weapon attacks. Here are many such examples as collected on SageAdvice.eu. A simple, specific one for easy reference:

Any unarmed strike counts as a melee weapon attack.

As such, the attack roll is calculated as follows:

  • d20 + proficiency bonus + Strength modifier
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