UPDATE
database1.table1 AS table1
SET table1.new_column = (
SELECT group_concat(old_column SEPARATOR ' ') AS 'old_column'
FROM database2.table2 as table2
WHERE table2.id = table1.id
GROUP BY table2.id
)
Conteúdo para você se capacitar em programação
UPDATE
database1.table1 AS table1
SET table1.new_column = (
SELECT group_concat(old_column SEPARATOR ' ') AS 'old_column'
FROM database2.table2 as table2
WHERE table2.id = table1.id
GROUP BY table2.id
)