This is adding to ulrich's comment. One reference for this result is the following article of Kollár.

MR1064874 (92e:14008) Reviewed Kollár, János(1-UT) Projectivity of complete moduli. J. Differential Geom. 32 (1990), no. 1, 235–268. 14D22 (14H10 14J10)

http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.jdg/1214445046

Edit. Although you did not ask about this, also Seshadri's criterion has been extended to algebraic spaces. Here is one reference by Cornalba.

MR1241126 (94i:14031) Reviewed Cornalba, M. D. T.(I-PAVI) On the projectivity of the moduli spaces of curves. J. Reine Angew. Math. 443 (1993), 11–20. 14H10 (14D22)

http://www.degruyter.com/view/j/crll.1993.issue-443/crll.1993.443.11/crll.1993.443.11.xml