The handover of documents took place at a ceremony two years after Sweden applied to join the military alliance following Russia's full-scale invasion of Ukraine.
Nato Secretary-General Jens Stoltenberg said in a statement on X that Sweden brings with it "capable armed forces and a first-class defence industry" and that the alliance had become "stronger and safer".
Sweden applied to join the defence alliance after Russia's full-scale invasion of Ukraine in 2022 - but its request was blocked by two members.
Hungary's Prime Minister Viktor Orban accused Sweden of being hostile to it and delayed its approval until last week, when the Hungarian parliament eventually voted to ratify the bid.
Mr Blinken recalled Sweden's 200-year policy of non-alignment which lasted until Russia invaded Ukraine, saying that Nato expansion was not "foreordained" or "foreseeable".
Finland formally joined in April last year, doubling the length of the alliance's border with Russia.
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