This is indeed true. I've seen God restore to me parts of me that I'd thought I'd lost. I've seen Him give me a new heart, a new mind. I've seen Him put new sinews into me, spiritually speaking, that weren't there before.
Titus (ESV) 5 He saved us, not because of works done by us in righteousness, but according to his own mercy, by the washing of regeneration and renewal of the Holy Spirit, 6 whom he poured out on us richly through Jesus Christ our Savior