You could create index using Index in __table_args__. Also I use a function to create ts_vector to make it more tidy and reusable if more than one field is required. Something like below:

from sqlalchemy.dialects import postgresql

def create_tsvector(*args):
    exp = args[0]
    for e in args[1:]:
        exp += ' ' + e
    return func.to_tsvector('english', exp)

class Person(db.Model):
    id = db.Column(db.Integer, primary_key=True)
    name = db.Column(db.String)

    __ts_vector__ = create_tsvector(
        cast(func.coalesce(name, ''), postgresql.TEXT)
    )

    __table_args__ = (
        Index(
            'idx_person_fts',
            __ts_vector__,
            postgresql_using='gin'
        )
    )

Update: A sample query using index (corrected based on comments):

people = Person.query.filter(Person.__ts_vector__.match(expressions, postgresql_regconfig='english')).all()

The answer from @sharez is really useful (especially if you need to concatenate columns in your index). For anyone looking to create a tsvector GIN index on a single column, you can simplify the original answer approach with something like:

from sqlalchemy import Column, Index, Integer, String
from sqlalchemy.ext.declarative import declarative_base
from sqlalchemy.sql import func


Base = declarative_base()

class Example(Base):
    __tablename__ = 'examples'

    id = Column(Integer, primary_key=True)
    textsearch = Column(String)

    __table_args__ = (
        Index(
            'ix_examples_tsv',
            func.to_tsvector('english', textsearch),
            postgresql_using='gin'
            ),
        )

Note that the comma following Index(...) in __table_args__ is not a style choice, the value of __table_args__ must be a tuple, dictionary, or None.

If you do need to create a tsvector GIN index on multiple columns, here is another way to get there using text().

from sqlalchemy import Column, Index, Integer, String, text
from sqlalchemy.ext.declarative import declarative_base
from sqlalchemy.sql import func


Base = declarative_base()

def to_tsvector_ix(*columns):
    s = " || ' ' || ".join(columns)
    return func.to_tsvector('english', text(s))

class Example(Base):
    __tablename__ = 'examples'

    id = Column(Integer, primary_key=True)
    atext = Column(String)
    btext = Column(String)

    __table_args__ = (
        Index(
            'ix_examples_tsv',
            to_tsvector_ix('atext', 'btext'),
            postgresql_using='gin'
            ),
        )

It has been answered already by @sharez and @benvc. I needed to make it work with weights though. This is how I did it based on their answers :

from sqlalchemy import Column, func, Index, String
from sqlalchemy.ext.declarative import declarative_base
from sqlalchemy.sql.operators import op

CONFIG = 'english'

Base = declarative_base()

def create_tsvector(*args):
    field, weight = args[0]
    exp = func.setweight(func.to_tsvector(CONFIG, field), weight)
    for field, weight in args[1:]:
        exp = op(exp, '||', func.setweight(func.to_tsvector(CONFIG, field), weight))
    return exp

class Example(Base):
    __tablename__ = 'example'

    foo = Column(String)
    bar = Column(String)

    __ts_vector__ = create_tsvector(
        (foo, 'A'),
        (bar, 'B')
    )

    __table_args__ = (
        Index('my_index', __ts_vector__, postgresql_using='gin'),
    )