Grace Roseman was found dead in her crib at her home in Haywards Heath, West Sussex, on 9 April 2015.
A coroner recorded a verdict of accidental death and said she died after becoming trapped on a bar.
NCT and Bednest released a statement saying they had reached a settlement.
The statement said: "Both NCT and Bednest as organisations unreservedly apologise for their respective parts in the tragic death of Grace Roseman and have reached a settlement on a confidential basis with the Roseman family.
"NCT and Bednest would like to make it clear that no blame should be attached to any member of Grace's family in relation to this tragic incident."
The cot was designed to be able to fold down fully, or partially, on one side.
Grace died when the cot was partially folded down and her head rested over the top.
At the inquest, which took place in December, coroner Penelope Schofield said she was unable to lift her head off and died of positional asphyxia.
She told Grace's parents, Esther and Gideon Roseman: "It must have been particularly harrowing for you to face accusations from Bednest that Pearl [the Roseman's other child] was involved in her death.
"But it was particularly unpalatable because there was no evidence on which to base that proposition."
Bednest said it had since modified the cot.
The parents of a seven-week-old baby who died in a Bednest cot have been compensated by the firm and the National Childbirth Trust (NCT) who co-branded the product.