Uber Technologies Inc. has completed a new round of funding that values the five-year-old ride-hailing company at close to $51 billion, according to people familiar with the matter, equaling Facebook Inc.’s record for a private, venture-backed startup.

Uber raised close to $1 billion in the round, one of the people said, bringing the San Francisco company’s total funding to more than $5 billion. Uber had briefed investors on a plan to raise between $1.5 billion and $2 billion in the round, The Wall Street Journal reported...