Я тебе верю.

Because верить normally takes the dative case for the person you believe or trust.

• ты = nominative, used for the subject
• тебя = accusative/genitive
• тебе = dative

So in Я тебе верю, я is the subject, and тебе means to you in a grammatical sense.

A very literal breakdown is:

• Я = I
• тебе = to you
• верю = believe / trust

Russian says it more like I believe to you, even though natural English is I believe you.

Верю is the 1st person singular form of верить.

That means:

• верить = to believe / to trust
• я верю = I believe / I trust

A few present-tense forms:

• я верю = I believe
• ты веришь = you believe
• он / она верит = he / she believes
• мы верим = we believe
• вы верите = you believe
• они верят = they believe

So the ending -ю here tells you the subject is I.

Yes, Я верю тебе is also correct.

Russian word order is flexible, so both are possible. The difference is mainly emphasis and flow, not basic meaning.

• Я тебе верю = very natural, common
• Я верю тебе = also natural, slightly more emphasis on the verb or the act of believing

Very roughly:

• Я тебе верю can feel like I do believe you
• Я верю тебе can feel a bit more like I believe you

In everyday speech, both are fine.

Yes. Russian often drops subject pronouns when they are clear from the verb ending.

So Тебе верю is a perfectly natural sentence.

Because верю already means I believe, я is not always necessary.

Compare:

• Я тебе верю = I believe you
• Тебе верю = I believe you / You, I believe

The version without я can sound a little more direct or contrastive depending on context.

It can be both, depending on context.

With a person in the dative case, верить кому-то often means:

• to believe someone
• to trust someone

So Я тебе верю can mean either:

• I believe you
• I trust you

The exact nuance depends on the situation.

Also compare:

• верить кому-то = believe / trust someone
• верить во что-то = believe in something

Examples:

• Я тебе верю. = I believe you.
• Я верю в себя. = I believe in myself.

Russian simply uses a different verb pattern.

The verb верить governs the dative case directly when the object is a person:

• верить маме = believe mom
• верить другу = believe a friend
• верить тебе = believe you

No preposition is needed.

But when Russian means believe in, it does use a preposition:

• верить в Бога = believe in God
• верить в победу = believe in victory

So:

• верить кому-то = believe someone
• верить в что-то / кого-то = believe in something / someone

The stress is:

• Я тебЕ верЮ

So the stressed syllables are:

• тебе́
• верю́

A rough English-friendly approximation is:

• ya ti-BYE vye-RYU

A few notes:

• я sounds like ya
• unstressed е is reduced in normal speech
• ю in верю sounds like yu

If you want to sound natural, make sure the stress falls on the last syllable in both тебе and верю.

Use вам instead of тебе.

• Я тебе верю. = I believe you. (informal, one person)
• Я вам верю. = I believe you. (formal one person, or plural)

So тебе is the dative form of ты, and вам is the dative form of вы.

This is a very common change in Russian depending on who you are speaking to.

Верю is the normal choice for a general present meaning: I believe you.

But related forms can change the nuance:

• Я тебе верю. = I believe you. / I trust you.
• Я тебе поверил. = I believed you. / I was convinced by you.
• Я тебе не верю. = I don’t believe you.

The verb поверить often suggests a change or moment of coming to believe, while верить is the ongoing state.

So for the simple sentence I believe you, Я тебе верю is the standard choice.