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有緣千里來相會 means that fate or destiny has caused us to meet from a thousand miles away.
The 有緣 part suggests something that is connected as if by a thread due to fate, destiny, or karma.
This romantic phrase is seen in Chinese greeting cards. It relays the idea that your love was meant to be and that you were destined to meet (regardless of what distance or obstacles might have made such a meeting unlikely).
See Also: Red Thread