Source of the expression בית עולמים referring to the temple

Question

Where does the term בית עולמים come from in reference to the Temple?

Answer 1

I don't know if it is the main source - but an early source can be found in the Mechilta

עד שלא נבחר בית עולמים, הייתה ירושלים ראויה לשכינה, משנבנה בית עולמים יצאת ירושלים שנאמר (כי בחר ה בציון) ואומר 'זאת מנחתי עדי עד' [תהילים קלב]

Before the Temple was chosen, all of Jerusalem was fit for (the reposing of)) the Shechinah. Once the Temple was chosen, (the rest of) Jerusalem was excluded. As it is written (Psalms 132:13-14) "For the L rd has chosen Zion … This is My resting place forever."

Answer 2

There are many examples of this expression in Chazal. The idea was probably derived from this verse in Kings

בָּנֹ֥ה בָנִ֛יתִי בֵּ֥ית זְבֻ֖ל לָ֑ךְ מָכ֥וֹן לְשִׁבְתְּךָ֖ עוֹלָמִֽים׃
I have surely built Thee a house to dwell in, a settled place for Thee to abide in for ever.