This script will generate the scripts you need to backup all of your databases to a specific folder (@sourcebackupfolder) and then restore them from a specific folder (@targetbackupfolder) on the new server. You could enable COMPRESSION in the backup if your server supports that.
declare @sourcebackupfolder varchar(255), @targetbackupfolder varchar(255), @targetdatafolder varchar(255), @targetlogfilder varchar(255)
select @sourcebackupfolder = 'c:\moving\', @targetbackupfolder='d:\moving\', @targetdatafolder='c:\sql\data\', @targetlogfilder='c:\sql\logs\';
select 'BACKUP DATABASE [' + name + '] TO DISK = ''' + @sourcebackupfolder + name
+ '.bak'' WITH INIT , NOUNLOAD , NAME = ''' + name + ''', NOSKIP , STATS = 100, NOFORMAT'
from sys.databases
where name not in ('master','msdb','model','tempdb');
select 'RESTORE DATABASE [' + name + '] FROM DISK = ''' + @targetbackupfolder + name
+ '.bak'' WITH REPLACE, STATS=100, '
+ 'MOVE ''' + (select name from master.sys.master_files mf where mf.database_id=db.database_id and mf.type=0)
+ ''' to ''' + @targetdatafolder + name + '.mdf'', '
+ 'MOVE ''' + (select name from master.sys.master_files mf where mf.database_id=db.database_id and mf.type=1)
+ ''' to ''' + @targetlogfilder + name + '.ldf'''
from sys.databases db
where db.name not in ('master','msdb','model','tempdb');