There are two ways to lift-over bigwig files from one genome build to another. One is using CrossMap or step by step as below. (CrossMap is almost the same to the break down steps)

CrossMap method: (taking from hg19 to hg38 as example)

pip install CrossMap

CrossMap.py bigwig hg19ToHg38.over.chain input.bw output.bw

genome liftover chain files can be downloaded here: http://hgdownload.cse.ucsc.edu/goldenpath/hg19/liftOver/ (change according to your needs)

Step by step method: (bw –> bedGraph –> liftover –> bw)

bigWigToBedGraph input.bw input.bedGraph

liftOver input.bedGraph hg19ToHg38.over.chain input_hg38.bedgraph unMapped

fetchChromSizes hg38 > hg38.chrom.sizes

LC_COLLATE=C sort -k1,1 -k2,2n input_hg38.bedgraph > input_hg38.sorted.bedgraph

bedGraphToBigWig input_hg38.sorted.bedgraph hg38.chrom.sizes output.bw

bigWigToBedGraph, liftOver, fetchChromSizes, bedGraphToBigWig are all UCSC utilities which can be installed from here: http://hgdownload.soe.ucsc.edu/downloads.html#utilities_downloads

Source:
http://hgdownload.soe.ucsc.edu/downloads.html#utilities_downloads
http://crossmap.sourceforge.net/#