Before you start

Estonian ID-card or residence permit card, ideally
Otherwise: documented proof of connection to Estonia
Passport
In-person attendance at a branch, for non-residents

Step-by-step

1
Choose a bank
Swedbank, SEB, Luminor and LHV all serve foreigners. LHV is the most e-Residency-friendly and the cheapest of the four for non-residents.
OnlineWho: You
2
Gather proof of your connection to Estonia
A signed residential lease, a signed employment contract, an enrolment certificate from an educational institution, or documents substantiating a connection to an Estonian company all qualify.
OnlineWho: You
3
Book an in-person appointment
Non-resident clients must be identified in person at a branch — digital identification is not available for this category, whatever your digital credentials.
In personWho: You
4
Pay the account opening fee if you're a non-resident
At LHV, opening costs €100 for EU/EEA/Swiss residents and €200 for everyone else, with monthly maintenance of €10 and €20 respectively. Card is €1/month, free under 26.
In personWho: You€100–200 opening, €10–20 / month
5
Set up Smart-ID at the branch while you're there
Smart-ID accounts can be created at a Swedbank, SEB or Luminor branch with valid identification if you can't verify with an ID-card. It's the key to every other e-service, so do it in the same visit.
In personWho: You

Documents you’ll need

Passport
Estonian ID-card or residence permit card, if you have one
Signed lease, employment contract, enrolment certificate or company documents as proof of connection
Proof of address

Things most newcomers don’t know

The e-Resident digital ID will not open you a bank account.

LHV states it plainly: the e-resident's digital ID is not an identity document and e-resident status by itself is not a sufficient basis for opening an account. Thousands of people get e-Residency specifically expecting Estonian banking and hit this wall. You still need a documented, evidenced tie to Estonia.

Source: LHV — non-residents

'Connection to Estonia' means a document, not an intention.

Banks want a signed lease, a signed employment contract, an enrolment certificate or company paperwork. Turning up with a plan and a passport does not clear anti-money-laundering checks. Sign your lease before you book the bank appointment, not after.

Source: LHV — proof of connection to Estonia

Non-residents cannot onboard digitally, in the world's most digital state.

It is the one conspicuous exception to Estonia's remote-everything reputation: non-resident clients require in-person identification at a branch. Plan a physical trip into the sequence rather than assuming you can finish it from abroad.

Source: LHV — non-resident identification

The branch visit is also your Smart-ID visit.

If you can't verify identity with an Estonian ID-card, a Swedbank, SEB or Luminor branch can create your Smart-ID account with valid ID in hand. Smart-ID then unlocks e-MTA, eesti.ee and digital signing — so one appointment can solve banking and digital identity together.

Source: ID.ee — becoming a Smart-ID user