By what mechanism is NADP+ converted to NADPH in Photosystem I?
OVERVIEW (verbatim from the article)


  Plastidic ferredoxin−NADP+ reductases (FNRs) accept electrons
  by two sequential one-electron transfer steps from two
  molecules of the one-electron donor ferredoxin to generate
  their fully reduced hydroquinone state, FNRrd, through the
  formation of an intermediate neutral semiquinone form, FNRsq.
  FNRrd then transfers both electrons as a hydride to the
  nicotinamide adenine dinucleotide phosphate (NADP+
  )
  coenzyme in a single step (Figure 1A).1,2


Theoretical Study of the Mechanism of the Hydride Transfer between Ferredoxin–NADP+ Reductase and NADP+: The Role of Tyr303 (Institutional access will be required!)

Basically, FNR is a flavoprotein with a stabilized FAD prosthetic group that can alternate 3 oxidation states with 0, 1 or 2 electrons. NADP+ binds in the FNR active site, and recognition of the AMP group causes a conformational change that brings the nicotinamide portion in proximity with the isoalloxazine group of the FAD. Ferredoxin is a single-electron carrier where two molecules of ferredoxin sequentially donate electrons to the FAD group that produces a hydroquinone FADH2. The actual architecture of the charge transfer complex formed in the active site mediates the formal hydride transfer that produces NADPH*. As far as I can tell, the hydride transfer occurs while the ferredoxin is still bound due to the effect electron transfer to FAD has on the pKa and protonation of a Glu312 that stabilizes NADP+ too much in the absence of ferredoxin (source). 

NADPH ends up getting released after the catalytic cycle.

*I'm still trying to find some more detailed information on the catalytic mechanism.