How to INSERT INTO one table from another table, WHERE

I am trying to insert data from 2 columns in tableB (colX and colY) into the same two columns of tableB, with a join
likewhere clause. Is this possible?  

For example:

INSERT INTO tableA (colX, colY)
(SELECT colX, colY
FROM tableB
WHERE
    tableA.blockname = tableB.block_name
    AND tableA.timestamp = tableB.timestamp)
;