Peter Abraham has a list of new draft pick signings, according to Damon Oppenheimer. He lists:

11. CF Ray Kruml (South Alabama)
12. RHP Luke Greinke (Auburn)
17. SS Addison Maruszak (South Florida)
18. RHP Brandon Braboy (Indianapolis)
20. RHP Patrick Venditte (Creighton)
22. RHP Corey Arbiso (Cal State Fullerton)
23. 2B Ryan Wilkes (Kentucky)
24. 3B Michael Lyon (Northeastern)
25. C Jeff Nutt (Arkansas-Fayetteville)
28. RF Chad Gross (Cuesta JC)
31. INF Spence Lucian (Princeton)
34. RHP Brad Rulon (Georgia Tech)
35. RHP Andy Shive (Azusa Pacific)
39. 1B Erik Lovett (Mt. Olive College)
42. LHP Clint Preisendorfer (San Diego Christian)
47. RHP Ryan Flannery (Fairleigh Dickinson)

Plus a pair of undrafted free agents: RHP Mike Obradovich from Florida Atlantic and C Ryan Baker from Cincinnati.

So, if those earlier reports are correct, the Yankees have signed a total of 18 draft picks.